Actually, though Wootz or crucible steel was by far the best blade steel available in ancient times, european blade and prod makers successfully made good-quality steel by hammering folding, heating, tempering, etc. Toledo Spain was famous for its high-quality sword blades as well as crossbow prods.
In fact, wootz steel required very different forging techniques from the iron available in Europe, so its entirely possible a skilled sword/prod smith in Spain might have made a total hash of working with wootz.
So by medieval European standards, it is possible for your local smiths to make good spring-steel even without access to true crucible steel. It will take longer, with different proceedures, but that's okay. In fact, with a little research, you could drop in a few tidbits about foreign-made steels. Since you're writing a fantasy, do as you like. 99 percent of your readers won't know or care. It's the narrative and characterizations that make a story wonderful, not your command of pseudo-medieval technology.