How to clean wooden mouthpieces?

Shogun.

「Stand User」
Been using my capsule mouthpiece for my tetra and noticed it's getting waxy in the wooden part. I got the glass insert soaking in smoke/vapor residue cleaner but I assume I shouldn't drop the wood in with it, does anyone know what I can use to clean that part?
 

passenger

is this thing on?
Soaking in acetone leaves the wood intact but it strips a lot of stuff that was former part of the wood(fats or whatever). It's a last resort method, but very thorough. If you do, let the acetone evaporate really good... and read up on it, it's not the nicest stuff...
 
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