Whether a standard length string works seems to vary by brand. But I think most brands' standard strings are actually usable for 15" to 16-1/2" violas even if they list a narrower range. The main question is not where the silk ends. It's whether the string needs to overlap itself on the peg, which with thicker strings may interfere with tuning and wear on the floor of the pegbox. If you can't get the string up to tension without overlapping more than one turn, the string is too long.
As for tone quality, whether the regular length and short length differ may depend on the brand as well. Some brands use the same diameter for all lengths, I've heard that some use a heavier gauge for short-scale strings. (I have no experience with shorter strings, the only two violas I've played have been 15-1/2" and 15-3/4".)
@Mouse and others. Since you want to purchase a new tailpiece anyway, why not get a 4/4 violin tailpiece and use it on your 15 inch viola. You will get the extra length you need and you will also get more string after length. Sounds like a win/win situation to me.
Success is the progressive realisation of a worthy ideal. —Earl Nightingale.