if you can remove all the stuff in that room. Cutting around and patching just makes the floor that much weaker, but its done all the time.
I would strive to remove ALL I can.
Then do your measuring and templating and cutting around then be sure to screw every thing down with Zinc or Galv screws. Screw down in a tight pattern, this will reduce or eliminate all squeaking and the bounces.
Say, even if you can pry up the fixture enough to slip in the new flooring that will also work.