In the C major blues scale, there's no F note.
The I-IV-V progression is C-F-G
Without resorting to the C minor blues scale, how do I improvise over a I-IV-V progression using the C Major blues when the F is not in the scale?
Simply put, you don't.
If anyone can find a single example of the major blues scale of the keynote being used over an entire I IV V I will gladly eat my hat. It is quite different to the usage of the regular (minor) blues scale where the keynote minor blues scale is often used over all the other chords. (eg E minor blues scale is used over the A(7) and B(7) chords in a blues in E.) I have never heard this done with the major blues scale.
The major blues scale is most commonly found in country and bluegrass music. If you are interested in learning to use it effectively then these are the genres you need to listen to and learn licks from.
If you are not interested in bringing aspects of these genres into your own playing then don't waste your time. Learning scales for the sake of it and not learning licks from their common uses in real music is a waste of time. For some reason of all musicians, guitarists fall into this trap most often. Probably more often than all other musicians combined! The world is littered with guitarists who learnt scales but never learnt how to use them musically (eg by learning from those who do use them musically)..But I digress..
You will find that the major blues scale is always used with the root of the scale as the root of the current chord. eg over a I IV V in C, C major blues with be used over the C chord, F major blues over the F chord and G major blues over the G chord.
Here's an example of it's use over a few chords in A:
(Timing is up to you)
It's a cliche sounding country blues licks consisting solely of the major blues scale of the chords used. A very common move in this style is to anticipate the chord changes, you can see at the ends of bar one and three notes from the major blues scale of the upcoming chord are used to introduce the chord before it arrives.
I doubt many of those who use it even bother to distinguish it from the major pentatonic scale. Country and bluegrass are so full of chromatic passing tones, it's already a given that any notes can be added in passing so there's often no need to confuse matters by introducing new scale names.
In most cases the C minor blues scale is exactly what you want. The ins and outs of this differ depending on the exact style you are trying to convey.
Try both of these and see how they suit you. The exact answer depends a great deal on exactly the style of music you are playing.
In general, if you are playing blues or rock (and it sounds like you are) you should focus more on vocabulary and phrasing
Vocabulary: This means having a repertoire of the appropriate material to play over the chords. For blues, the best thing to do would be to learn the solos of other blues players. You can do this from a book, or by ear. You will find that in many situations the players will not exactly play the scale that is theoretically correct. Bends, and little chromatic ornaments are a big parts of blues playing. Many players will even play with notes that sound quite wrong for the sake of tension.
Phrasing: This is how you play. If you play the correct scale, but stiffly, it will still sound wrong. Again, listen to the masters of the style you are trying to emulate. The small inflections, slurs, taps, whatever they put on the note will make the difference between lively music and a technical exercise.
You may be confusing the blues scale with major pentatonic. This pentatonic has C D E G and A, so no F (or B).Taking those out of a major scale removes opportunities to play really bum notes anywhere. Nothing will clash with I, IV or V in a violent way.
The standard blues scale notes are C Eb F Gb G Bb. Of which 3 are certainly not in major.They are bum notes, but in such a bad way that when played 'properly' will sound more than just good. Sort of 'sweet and sour'.
However, most blues players will use a combination of blues and maj. pent. in their playing. And other notes that wouldn't appear in either. Basically, if you know what you're doing, every note in the chromatic scale is ripe for use in the blues.
Example - C blues- C Eb F Gb G Bb. F blues- F Ab Bb B(Cb) Eb. G blues - G Bb C Db D F. All that doesn't feature are E and A. But since they are the major 3rds of C and F, they are often bent into from the Eb and Ab. So they all get an airing at some point.
This is not the time to go on about how to play - you asked about certain notes. I hope this makes it clear enough for you to go off and use them !
EDIT: Major Blues scale on C = C D Eb E G A , again no F or B. However, Maj. Blues on F = F G Ab A C D and on G = G A Bb B D and E. So no C# and F# available if one uses the 3 scales for the 3 chords. These maj. blues scale notes relate to the relative minor blues scale. As in C maj. blues = A blues notes.
Scales are just a starting point. Play with the scales major or minor pent. Are you playing over dominant 7 or 9 chords, you can try Mixolydian modes. I started by using just the minor pent of the I chord, then I started adding the major pent, then messed with Mixo mode. However, thinking about switching scales seemed needlessly complicated to me so I just combined them. So it's 1,2,b3,3,4,b5,5,6,b7, but you have to be aware that not every note always sounds good over every chord. You have to just play and you learn when to use which interval. I know it seems like a ton of notes, and actually when you add the notes from the IV and V its all 12 notes, but you're not going to be playing them all the whole time. Really focus on the intervals and you'll hear right away what sounds "right", like putting a little curl on the b3 when you're stepping down from the V IV to the I. Emphasize the chord tones; that doesn't always have to be the root of the chord. Bending the b3 into the M3 of the I chord is great. The M3 of the V is a 1/2 step from the root of the 1, you can bend or slide between them on the change. There are so so many different things you can do to accentuate the change. Play major notes over the I for the 1st four bars, then minor when it comes back around. Playing notes out of the chord can add tension. So many things, I'm rambling now, just really learn the intervals and accentuate the chord tones. Write out what works and you'll play without thinking, which is what you want.
You've gotta kind of ignore the chords when playing pentatonic or blues scales, since they don't have all the notes of the chords, but still sound really good if you've got a proper melody. if you want though, you still can emphasize every other note in the F chord (A, C, Eb), but it's usually better if you just think of the melody and the chords separately. Just emphasize the C, G, and E (in order of importance) the whole time and you're good. You can always play C blues on C, F blues on F, and G blues on G or any scale that works with each chord (it's usually mixolydian), if you want to be super technical, but it's fine to just think of the melody and chords separately.