Some ideas:
Use git mergetool
to split the merge files into original and new parts. Hopefully one of those is the file with your non-stash changes in it.
Apply the diff of the stash in reverse, to undo just those changes. You'll probably have to manually split out the files with the merge conflicts (which hopefully the above trick will work for).
I didn't test either of these, so I don't know for sure of they will work.