Cleaning up Lapping Compound?

What's the best way to clean up the lapping compound after lapping rings? Obviously I can't remove the lower half of the rings to clean them up easily. So whatever is used need to be safe for the gun's finish. I usually just wipe it up with paper towels and then use a gun cleaner sprayed on a paper towel. Is there a recommended way to clean it up?

Damp/wet paper towel followed by another damp/wet paper towel. Repeat if needed.

I find that a coarse rag removes a good amount. I follow that up with another rag with solvent then use a fine rag to clean it up.

I like to finish with a paper towel to soak up whatever is left and run q tips through the bolt holes to get the junk out of there before putting the threadlock on it.