Just
I don't know if this will work, but
if there is /usr/bin/startmate and startcinnamon,
you can put something like
cp -f "$HOME"/.local/applications/mimeapps.list-mate "$HOME"/.local/applications/mimeapps.list
and the same for Cinnamon.
Still remains the problem at logout, you must save mimeapps.list as mimeapps.list-mate(or cinnamon)