If you’re carving a bowl, most of the surfaces currently covered in wax will be carved off anyway. I’d scrape off what you need to to see what’s going on, then just plane your top surface clean as the wax won’t have penetrated much if at all.
Mineral spirits (White spirit here) will likely soak in quite a lot, which could spoil a finish, though if you plan to finish with oil as is usual for wooden bowls it won’t be a problem.
Save yourself some time and money by not cleaning wood that is going to end up as chips on the floor!
Matt