[Arran]

Is the finish on the cabinet in good shape or is it a bit tired? If it's in good shape I would try cleaning the finish with Gojo, just in case it's on the surface, reflowing would only bury the dirt in the finish unless you clean it first. You could also try it on the inside, or spray it with brake cleaner. If push comes to shove, you may have to wash the inside of the cabinet out with TSP, but that would involve hot water, so stick with washing the inside bottom this way, and dry it quick with rags and a heat gun.
Regards
Arran