Even though the sport is commonly called "Cowboy Action Shooting", you really just need to dress in "period appropriate" style (or "Hollywood" impression of same) - not necessarily as a wrangler or gunfighter.
Many really imaginative shooters go for some other look entirely - e.g. military, farmer, townsperson (whether storekeeper, gambler, saloon girl, doctor, whatever) and so on - then you can be perfectly justified in such things as wearing much more comfortable lace-up shoes or ankle boots, which are potentially also much more affordable (especially if you can locate something suitable at a thrift store) ...