It's certainly POSSIBLE, but would require a bit of work. At the very least, the texture of the modern uniform will have to be applied to the old-style tshirt uniform, which may cause a problem since it is open at the neck. There may have to be a new uniform model designed which has short sleeves but that collar at the neck.
I have actually been looking into this in some detail, and basically there is a separate "skin" model for all the different uniforms that show skin. An open neck, exposed midriff, and exposed arms, each has their own individual "bit" that is fit together to form the uniform. I guess that's to eliminate clipping. So basically, it wouldn't just be a matter of substitution, I think a whole new uniform will have to be designed.
Personally, I'd be for this. I think in the canon most of the uniforms had long sleeves (you could just take off the jacket if you "had to get your hands dirty") but I think it should be a usable option, even if rarely used.
I fully support anything that adds additional options to our uniforms/costumes. As far as canon goes, I remember one specific instance of shorter sleeves. Before the DS9 crew switched to the First Contact uniforms in "Rapture," Chief O'Brien usually wore his uniform with the sleeves rolled up, which makes sense since he's usually crawling around the Jeffries Tubes.
Come to think of it, that would be another cool addition to the uniform options... :p