hello eppersrn, welcome to GWOF. if the faux wood is held on like the plastic chrome then there is two sided tape holding it on and a heat gun should get warm enough to get the glue soft enough so you can get the faux wood off the bike
I would think if you were sure to clean any wax and sanded it well , then primed and painted it would be fine.
If it's held on with double sided tape. You might be able to loosen it up using a heat gun or hair drier. Then clean up the plastic with rubbing Alcohol.
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