When you say "wooden handles" do you mean like a sort of toggle grip/straight piece of wood to hold on to?
I would guess that as long as the wood was smooth, there's no reason to change them at all.
Handles with a bit of weight to them that you hold rather than wear are really nice, especially for things like throws or hand-swaps. They also have the advantage, as you mention, of being easily-"dropable" incase of a tangle (very important when using fire).
The only real disadvantage I can think of is that it will tire your hands more as you need to actively grip them - finger loops or wrist straps just stay on your hands. Also, if the wood isn't smooth or your hands are a bit sticky (?) you'll end up with blisters - but constant use will build up callouses so this won't be a factor after a while.
Ultimately - if it works for you...it works!
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