If you go by Voyager, nanoprobes assimilate by grasping onto blood cells and injecting stuff into them, and they control minds by directly interfacing with a humanoid nervous system. I find it highly unlikely it would work on a changeling.
I find it unlikely it would work on a human
. The super-fast zombie-like borgification was added for First Contact, and although it adds to the movie-length danger, I find it annoying. Of course, the the-only-thing-we-can-do-is-assimilate also comes from FC and VOY, so...