I found that using Brake Cleaner to remove bullet lube from a die absolutely does leave a residue. It simply dissolves the grease and leaves a film of grease.
This calls for Mr Guffey's towel and a dowel approach
Ok, brake cleaner is a non residue leaving cleaner. None.
Any petroleum based solvent leave behind a film, all by its lonesome. Hopees etc, Stoddards, thinner etc.
So yes, you do need to use a paper towel, paper shop towel (blue) or a clean rag (any color) to removed what you have dissolved. You need to be sure said towel does not have other residue on it.
If you do so there is no residue left form the Brake cleaner and if there is a residue its not cleaned off grease dissolved.
You can also use FD cleaner, which is better than todays brake cleaner and as good as the former available but no longer TriClorethalene (sp) (aka TriChlore)