If your fit-up is good enough, then you can just fuse it. Don't know if you have much stainless experience, but, it MOVES when hot. 4-6 tacks around the circumference at a minimum. The diameter of that pipe, I'd probably aim towards 10-12 myself. Figure the wall thickness is ~0.058, so 60 amps is plenty. Full pedal mash it, tack, kill the pedal. Keep your torch over it for 10 seconds for postflow to prevent infiltration of impurities. Your tack should come out close to gold in color if you've had sufficient gas coverage.
For 321, I'd use 321 wire, or at least 316. If you hit the welds promptly with a clean stainless brush, you'll remove the color almost completely.
So for a down-dirty purge, plug the header end with aluminum foil balls. Tape up the tailpipe end with numerous criss-cross pieces of Blue Tape. Make your tacks. Then poke a hole in the tape and just run gas from your torch into the pipe for about 3-5 minutes, header above your welding. It will be more than adequate for what you're doing.