I'd knock off a bit of the
thread sharpness with 600 wet or dry paper first, then maybe grab some buffing compound for stainless steel and go to town on the
threads a little at a time till they threaded without much force.
As long as you don't cross thread the parts will screw together better after a lot of use, the sandpaper and polishing compound are just trying to clean up 0.001" or maybe 0.0001" imperfections not major threading problems.
As long as the threading is the same (which it should be) you should be able to get the parts to screw together with a little cleanup of the threads.
You can also get chromium oxide paste or in bar form to help accelerate the polishing of the threads, coat the threads with a small quantity and beginh working the parts on and off as much as is needed to smooth them out. You may want to clean the threads every 5 or 10 passes to get a better idea of your progress. There is not a huge quantity of skill needed to get the threads buttery smooth feeling (they may not look great on very close inspection, that depends on how bad they were to begin with), just add a bit of push or pull as you thread the parts together (just like you would for a child safety cap). This helps quite a bit in my experience when polishing threads.
I wouldn't use diamond abrasives unless the fit was truly way too tight and even then I'd be extra careful as diamond is a very agresive abrasive.
Maurice