[must.... resist.... suggesting... silicone sealant...]
The main requirement seems to be something that dries with the same volume it had when wet, or else something that can be easily trimmed if it dries with greater volume. The space-filler foam can be easily trimmed to make a flat surface, and its brittleness shouldn't matter if you're just filling in a couple of holes that will be surrounded by handle foam and covered by grip and overgrip.
I believe putty comes in different densities, and a little weight added underneath the hand shouldn't have noticeable effects on playability.
You might also go to a Michael's, or other hobby store, and get their advice on the matter. Good luck!