I love love love that you did a fun cosplay at the theatre!
I use inexpensive synthetic wigs for costuming - Halloween, cosplay events, theatre. Synthetic wigs can be washed by very gently swirling in a sink with a very little bit of soap. I think I’ve used a few drops of baby shampoo in the past. . I use my fingers to try and detangle the wig before I get it wet. If it’s a smooth wig, I brush it gently with a plastic bristle brush, such as a doll brush. DO NOT COMB OR BRUSH A WET SYNTHETIC WIG.
Wearing a wig cap helps keep the wig clean for longer. They’re usually a couple bucks at your locally owned beauty supply store, or you can cut the bottom of the leg off pantyhose and use that.
I let the sink drain, and blot it carefully with a smooth t shirt or microfiber towel. I carefully reshape any curls with my fingers, and let it dry flat on a counter. If it’s long hair, I’ll hang it on a towel hook.
For styling synthetic wigs, I’ve used warm (not hot!) hot rollers. And I don’t think you’re supposed to do this, but I use a teeny bit of hairspray. These are on cheaper wigs. I haven’t ventured into real hair or expensive synthetic wigs.