I do think what I am about to say will not be good. I have performed this cleaning up chequering twice after the finish was applied liberally to the chequering, to remove it by cleaning each individual line is time consuming and tedious at best. Also there is the case of a slip with the checkering tool, not to mention the differing colour between the rest of the stock and the newly cleaned the chequering. To save all that angst and soul destroying repetitive effort strip the stock and chequering and re finish the stock, or get someone else to do it.
Either way it will be a painfull experience.

Good luck witch ever you decide to do.
Ernie


The only lessons in my life I truly did learn from where the ones I paid for!