It may be better to dedicate the double boiler to your wax melting. the outside pan, containing only water is not a problem. Removing wax can be done pretty well if while the container is hot and the wax is liquid, you use a paper towel. Go over it a couple of times. I’m talking here about removing clean wax, such as you would use when you make candles.
If you are referring to cleaning a pan in which you had all the gunk of a brood nest comb, the procedure is similar, but you need more “elbow grease”:
Remove all you can from the pan and toss in a few handfuls of sand. You may put it directly on the burner to keep it hot. With gloves so as to not burn yourself, rub the sand all over, until you feel that all the gunk is loose. Toss the sand and proceed with the paper towel as before. It may even be clean enough to put in a dishwasher.

With that said, it probably doesn’t matter all that much, since the presence of both wax and oil helps protect the wood.
Thanks