Does this mean I can't claim to be palm oil free?
I can't help you much with the carnauba itself (except that I somehow have in mind that you might have a look at
rice bran wax or
sunflower wax instead).
But just so much wrt palms: coconut palms are palm trees too, and if you're pedantic about “no-palm”, you would have to ban coconut oil from all your items as well, and you would have to resort to laurel oil to get some lauric bubble boost into soaps.
ETA: Nitpicking about the meaning of “palm (oil) free”: If you refer to it as not containing palm oil in the narrowest sense (the oil extracted from the pulp of palm fruits), then you're entirely safe. So are you if you want to boycott anything from
Elaeis guineensis (including PKO, many vitamin E concentrates, carotene colourants, and palm kernel shell charcoal). AFAIK, the carnauba palm
Copernicia prunifera is native/limited to the Caatinga ecosystem of northeastern Brazil, and cannot compete with rainforest for this reason (Like with everything, there is for sure valid ecological critique on the exploitation of these palms, but I have no overview over them). And in the end, it's a
wax, not an oil, so not even the hypocritical plate-tank hysterics apply.
in my soap, except I do with goat milk…so it’s not vegan..I don’t use palm because I’ll dream of monkeys, but I use soy wax and I think of mutants 
. I’m just rambling, but I sure appreciate you and everyone else on this forum respecting every soapers choices for whatever reason. One of the things I have learned here is the ‘civilians’ have no idea how the soapmakers’ brains work 
