I have also dabbled in tempering chocolate, but have never been able to get something that you could hold for a while without melting in your hands. I've also never tried coating ice cream bars.
I think you should be able to do it with a high fat(butter, cocoa butter, coconut oil) chocolate mixture. It will probably seem like entirely too much fat, but that is going to firm up and become a shell when wrapped around something cold and creamy. Here's a recipe for "magic shell" (I'm sure that is actually trademarked by Hersheys) that that goes something like 2:3 cocoanut oil to chocolate. That should give you something that resists dripping down your hand.
Then again, you could always just make ice cream pops instead. Just shove a popcicle stick in it and you have clean hands, but that's not what you asked.
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.
Best Answer
You'll want to temper the melted chocolate. This means holding it at 88° F (31° C) while it cools until it is completely hardened, then finally allowing it to return to room temperature (or lower) afterward.
If you temper the chocolate this way, it will be much harder and last indefinitely at room temperature.
The easiest way to temper chocolate is the "seed method", which means adding a piece of solid (never-melted) chocolate to the fully-melted chocolate after removing it from the heat source and stirring thoroughly until the temperature reaches 88° F / 31° C, and then keeping it at that temperature until you're ready to use it.
(Note that this is for dark chocolate; for temperatures for other types of chocolate and for a more detailed guide to tempering, I suggest you check out the tempering page at Cooking for Engineers.)
The technical explanation for this is that the temperature at which melted chocolate hardens determines its final consistency as a solid. If chocolate hardens at room temperature, it ends up forming a very weak crystalline structure that begins to melt at even the slightest rise in temperature (i.e. in your hand). Allowing it to solidify at the highest possible temperature below the actual melting point ensures that it forms a denser crystalline structure and will not melt at room temperature.