If you insist on skipping the first and sixth string, you will find it easier to do if you strum by anchoring the heel of your strumming hand right behind the bridge and strumming with a short sweep of the wrist as opposed to moving your entire arm. Or anchor your forearm on the top edge of the guitar and keeping the heel of your hand on an imaginary fulcrum point, strum using an up and down sweep of the wrist - keeping the size of the sweep just wide enough to cover the 4 strings.
BUT - I am not sure why you feel the need to mute the first (thinnest) string when playing an A shaped barre chord. It is common to fret the high e (first) string with the first barring finger and play the corresponding note which will give you a repeat of the 3rd note of the major triad an octave higher. But it will still always be a note in the chord the same way the note played on the 5th string is a repeat of one of the 3 notes in any major chord played using an A shaped barre chord. I always extend the first finger barre all the way to the high e string and play that note as part of the chord.
Also, it's less common to do so, but still acceptable to also fret the first (fattest/low E) string in an A shaped barre chord as this will give you a repeat of the 3rd note of the triad an octave lower instead of an octave higher.
This is not much different that playing a 6 string E shaped barre chord where common practice calls for barring across all six strings with the first finger thus catching both the low and high E string on whatever fret you are barring. The note on any given fret of both the high and low e-string will be the same note - only separated by two octaves. Said note will be one of the three notes contained in either an E shaped barre chord or an A shaped barre chord.
So to make things easier, I always fret all six strings when playing an A shaped barre chord. Then if I accidentally hit the low E string, it sounds okay because it's a note in the chord.
There are only three separate notes in an A major chord or any A shaped major barre chord. Thus an A shaped barre chord can be played with 3, 4, 5 or 6 strings and it will still be the same chord. Any more than 3 strings and you are repeating at least one of the 3 notes in a different octave. In most cases I find that 5 or six strings included in a chord sounds fuller than 3 or 4 - not to mention being easier to play when you eliminate the need to "miss" certain strings.
Good luck with whatever method you choose to incorporate into your individual playing style.