I don't have/want to use capo for my guitar.
Can a specific tuning be applied as an alternative to capo?
It entirely depends what you want to play.
A capo is for transposing a piece up by some number of semitones, without changing the fingering. So let's look at ways to transpose those pieces without a capo -- it will often involve changing the fingering:
If the piece does not contain any open strings, you don't need a capo. Just play the piece with your left hand higher up the fretboard.
If the piece contains a few open strings, you may be able to finger the piece a different way -- whenever the original had an open string, you'll need to fret it. Often you can achieve this with a barre. In this case your index finger is being a "capo" temporarily.
You could tune all your strings up by whatever interval you're transposing. But note that tuning up by more than 3 semitones puts you at risk of breaking strings (and when this happens, cutting flesh), or damaging your instrument's neck.
You could accept different chord voicings. For example, if your original involved strumming the chords D then G, and you're transposing up by 2 semitones, then you could play the chords E then A, including open strings. It will sound different, but it would still be an acceptable accompaniment to a song.
There are transpositions that can't practically be achieved without a capo.
Consider this chord:
The fretting is all on the 6th and 7th fret, but there are also three open strings. If you tried to transpose this up by 3 semitones, without a capo or retuning, you'd have to finger the 3rd fret, as well as the 9th and 11th fret. Nobody's hand is that big!
You don't explain why you don't want to use a capo. If you want to achieve what a capo does, then a capo is the best way to do it.
For the sake of a thorough answer, there are some new electric guitars that have recently appeared on the market that make use of what is refered to as a "digital capo". They can be configured to use built-in digital signal processing to raise or lower the pitch of the strings by digital pitch-shifting, while the actual tuning of the physical strings stays the same. So the notes coming out of your amplifier are different than the acoustical notes played by the strings themselves.
Getting one of these guitars would be expensive as they are rather esoteric instruments. The pitch-shifting technique is not entirely natural-sounding.
A set of light strings, tuned a few semitones sharp, will have a similar tension to a set of heavier strings tuned to concert pitch. Consider the following two sets of strings:
.009 .011 .016 .024 .032 .042 -- A "light" set .012 .016 .020 .032 .042 .054 -- A "heavy" set
The "E" string of the first set and the "A" string of the second set would both be interchangeable. A guitar wouldn't care whether that string was put in the sixth slot and tuned to "E", put in the fifth slot and tuned to "A" [five semitones higher], or put in the sixth slot but toned to "A". The pattern doesn't quite continue on the higher strings, so tuning a light set up a full five semitones might be a bit of a stretch, but tuning up four semitones should not be at all unreasonable if one is using a light set of strings to start with.