Since the cones are metal, they can likely stand some heat. Place a dry paper towel on the spot where the residue is — make sure it's touching the residue — and use a hair dryer to heat it up. Any remaining residue should wick into the paper towel.
I'm not 100% sure this won't damage anything, so it might not be a good idea....
If you use a paper towel just be careful that the paper towel doesn't get left behind on the cone... that was why I suggested a rag rather than a paper towel to hopefully avoid leaving behind any bits of paper towel.
Either way it's a bit of a crap shoot - if you're married, my best advice is to ask your wife. She probably has better ideas than all of us.
Jason
