tl;dr
Run git add first.
I just discovered that if your uncommitted changes are added to the index (i.e. “staged”, using git add ...), then git stash apply (and, presumably, git stash pop) will actually do a proper merge. If there are no conflicts, you’re golden. If not, resolve them as usual with git mergetool, or manually with an editor.
To be clear, this is the process I’m talking about:
mkdir test-repo && cd test-repo && git init
echo test > test.txt
git add test.txt && git commit -m "Initial version"
# here's the interesting part:
# make a local change and stash it:
echo test2 > test.txt
git stash
# make a different local change:
echo test3 > test.txt
# try to apply the previous changes:
git stash apply
# git complains "Cannot apply to a dirty working tree, please stage your changes"
# add "test3" changes to the index, then re-try the stash:
git add test.txt
git stash apply
# git says: "Auto-merging test.txt"
# git says: "CONFLICT (content): Merge conflict in test.txt"
… which is probably what you’re looking for.