Real chocolate (cocoa solids, cocoa powder, and sugar) is not the best thing for what you want. If properly handled, it can give you a great tasting glaze - but you don't have the conditions to handle it properly (slow cooling), so you will run into problems with it (bad texture, sweating, bad looks/dull). Also, it won't be a really snappy shell. And at this temperature, the good flavor is not very noticeable anyway.
What you want to use is cocoa-containing fat glaze. This is the stuff which commercial "chocolate" coated ice cream like the Magnum brand uses. It is sold in supermarkets as "chocolate cake glaze" and similar names, but check the ingredient list to be sure. It should consist of cocoa solids and vegetable fat, possibly some emulsifiers too.
You should only melt your glaze, preferably have a low-temperature water bath at your booth (not full boil), and hold the glaze there for dipping. Don't add milk at all. Milk is a bad choice for chocolate covering anyway. Cream is used for making cake icings called ganache (mixed with real chocolate, not this glaze stuff), but it makes a soft, smeary icing, not a hard, snappy shell. Use the glaze the way it is, without adding anything.
This glaze is quite hard at room temperature already. A thin layer of it on a frozen banana should go to below room temperature almost instantly. I think you will have your shell without any special preparation. But I have never done it this way, so I would advise you to experiment. If my hunch is wrong, there still isn't anything you can add - this stuff doesn't harden because of anything added, it hardens because at room temperature, it is a hard solid. So your only way to speed hardening is to return the banana to the freezer for a short time. But then you are likely to get a condensation problem, so keep it as short as possible.