What about a light delta mush on the skin? would have to be heavy enough to relieve the low poly driver artifacts, but light enough not to blow away your nice wrinkles.
Is the fat/skin coupled? Not much you can do in this case except upres the fat and rebuild your setup.
If not coupled, you could create an intermediate mesh that is higher resolution than the fat. Maybe even it's a copy of the skin. Wrap that to the fat bake and deltamush it (lightly, just enough to remove the artifacts). Use the deltamushed version as a bone to drive your skin wrinkling