I have a collapsed arch in one of my feet that makes repeated jumping or low-stance work quite painful. Some instructors are not fond of students wearing shoes (even if designed for martial arts use) with orthotics because the orthotics are still hard and can injure another student's feet if I accidentally stepped on them. I have prescription orthotics but could probably wear an alternate form of arch support for the couple of hours I'm in training. Obviously I will need to respect an instructor's wishes, but what can I do to minimize problems? Are any specific types of shoes and/or arch supports favored over others? What about taping techniques designed to minimize pain (I've heard that dancing schools use special taping techniques but have not seen it in martial arts).
This is going to be something of a trial and error method for you, I think. You're going to have to try a bunch of things and go with what works the best or sucks the least.
First of all, if your instructor outright bans shoes, that's one thing. If your instructor says no shoes "because" of some reason, then you have a little wriggle room. In that case, see if you can find shoes that don't go against that reason. Once you can wear some kind of footwear, it opens the door to adding orthotic inserts, which is what you want.
There are many "minimalist" shoes around now. They have a flat insole mostly, with a very little amount of rubber on the outside. They weigh so little.
But, the problem with minimalist shoes is that they're still fairly bulky and introduce a wide, hard edge on the outside, along with a deep tread on the bottom and squishy foam on the inside. That doesn't fit in well with barefoot martial arts.
So one thing you can do is to look for shoes that are so minimal that they feel like they're painted on your foot, or that the edge is removed or tucked under.
For example, the Vibram Five Fingers shoes. Try a pair of these on, and see what I mean. Make sure your toes fit snugly and have very little room in them.
Vibram shoes alone might work for you, believe it or not. You may find that's all it takes to make your life a lot better. And your instructor may actually say it's okay. There's no hard edge, no bulk to it. It's like having an outer skin, that's all. And if you make it clear that you only intend to wear them at the school and not outside (so it's not dirty), then that might work. Even suggest that you keep them at the school, so there's no doubt that they're for class use only.
If Vibrams don't work much for you, then you might need to try other shoes. I don't think you'll have complete success stuffing an orthotic insert into a Vibram shoe, but you can try. Their web site specifically says they're not made for orthotic insoles.
There are other shoes that are popular in martial arts like Taekwondo and Wushu kung-fu. For example, FeiYue ("flying fish") shoes. They're really cheap and weigh very little, but they're not as "painted on" as Vibrams. And they do have a blocky edge, even if it isn't very hard. Those you can add inserts into also.
Another good shoe is something like an Addidas martial arts shoe. Those are used a lot in Taekwondo. They're pretty soft and don't have a hard edge on them.
As for wrapping your foot, that may help also. Worth a shot. They even sell arch wraps. For example, the "Mueller Arch Support" wrap. Maybe your instructor would be fine with those. You probably won't get much support from it, but having the wrap there will give you feedback on how well your foot is doing. That can make you more conscious about it, so that you get better at not letting your foot completely collapse into the arch. (You can try rolling your weight forward onto your toes / ball of the foot when you feel it.)
You could also place a squishy foam insert into the inside of the wrap also. I mean, not between your skin and the wrap, but inside of the wrap itself. Open it up, insert the foam, and then stitch it back up. That way, you don't have to worry about the insert coming out and flying off during practice.
And almost certainly, your instructor wouldn't have anything against this option. It doesn't cover the entire foot, just the arch, and very minimally so.
About the only problem you might have with a wrap like that would be traction. You might slip. So, you can deal with that by coating it with something that causes it to grip more. Try a product called "Plasti Dip". It's perfect. You can also use "Puffy Fabric Paint" and other products. Even "Sugru" might work.
No, dancers don't wrap their feet in a way that would help you. Their purpose is to wrap it so that they can point (for ballet). That's where they stand on their toes. It's not for arch support. It's to keep their toes from sliding out. And I might add that it's crazy what dancers do to their feet! That is, if that's what you were thinking of.
Anyway, hope that helps.
I believe I have might be able to help. My chiropodist and I have been working on a martial arts orthotic device for several years now. We have created a barefoot sports (martial arts etc.) arch support based on a ankle sleeve support concept, so it's not a shoe and the orthotic arch support is a medium density EVA foam shaped specifically to offer support in either hardwood or foam tatami dojos. I will be testing this product this february and I hope to start production this spring.