This is a good question, and one I've never considered.
I've looked through the rule book and there does not appear to be any rule addressing this specifically. Since it is not addressed, it is safe to assume that it is indeed legal to change racquet hand/free hand during a game, and apparently even during a point. There
There are specific rules that apply to raquet hand and others to free hand, but there is nothing specific about that being a static thing (unchanging).