You took the words right out of my mouth. The workaround for this issue is to listen to what the announcer says before the fight and he'll let you know what kind of fighter you have. Adds a few more seconds before you can start your fight, but I think its worth it (if you don't mind looking at the intros all of the time, especially when you're introduced second).
Of course it doesn't help if you want to know what style of fighter you're choosing during the select screen, but for me, thats kind of the fun of it all. Keeps me on my toes and forces me to learn to play with all of the styles, SURPRISE you have a wrestler, good luck (I can't stand fighting with wrestlers by the way)