Hi Adam,
Welcome to the forum.
Although the TK16 is a BKA-approved kendama, I think the custom paint job would have to count as it being modified, so unfortunately for you, it's not allowed. We do have the rule that competitors have to own their own kendama, but I think in this case you would probably be allowed to borrow a kendama from a friend (or us) to compete with. After all, we want to be *in*clusive, not exclusive.
Cheers.