If the assy is open, and witht he copied part open in it's own window,use the Save as function, but be sure to select the Copy option.
After saving, return to the assy and use the Replace Components with the All Instances option NOT selected, to switch the copied part to the newly saved part.
When you save an assembly as a part you also have some options. You can save all the bodies or just the outer surfaces and you can also decimate those surface IIRC.
