I have flat, wide feet, and tae kwon do classes are starting to hurt. I'm thinking to try wearing shoes with my running orthotics. Are there specialty martial arts or wrestling shoes that are wide and structured in a way that would accommodate an orthotic? What should I look for in these type of shoes?
You could give Vibram FiveFingers a shot... I would't recommend anything with a thick sole, as that will probably lead to injury down the line.
Or you could try tabi, which are used in some dojos in Japan. They are sort of a crossover between socks and shoes. You can get them with or without a rubber sole.
I've been in a similar situation for most of my life, very wide feet and orthotics. I train in a school that wears shoes to train, so I've seen a lot of solutions.
You might try looking at indoor soccer shoes (might work, but not made in my size). I ended up with New Balance walking shoes, which are orthotic friendly and aren't very aggressive in the tread.
It could be that your feet will just get used to it, too. I've trained barefoot as well, and it wasn't a big deal after a while.
I dont think they sell shoes by width. if you really want the perfect width, then you'll probably have to get some shoes custom made, which will probably be expensive. however, you should probably check out http://www.karatedepot.com/martialartsshoes.html first if you havent already. they have good stuff.