I’d do it with cherry-pick -n (--no-commit) which lets you inspect (and modify) the result before committing:
git cherry-pick -n <commit>
# unstage modifications you don't want to keep, and remove the
# modifications from the work tree as well.
# this does work recursively!
git checkout HEAD <path>
# commit; the message will have been stored for you by cherry-pick
git commit
If the vast majority of modifications are things you don’t want, instead of checking out individual paths (the middle step), you could reset everything back, then add in what you want:
# unstage everything
git reset HEAD
# stage the modifications you do want
git add <path>
# make the work tree match the index
# (do this from the top level of the repo)
git checkout .