Instead of removing the fat, I would render it by propping the chops up, vertically with the fat lying in the pan, until it is browned and the pan has a layer of runny fat in which to cook the chops, instead of butter. Or cut the fat off, if you must, and render it in the pan before cooking the chops in it.
Then proceed following Steve's/Delia's instructions.
Don't worry about your fat consumption - you are going to cook the mushrooms in butter anyway, and then add cream.