Tig will do the job.

If I had a tig I could do it. I was a pipe welder before I started a company.

Problem is tig takes a lot of practice with a lot of materials. And then stainless is a little bit trickier than carbon steel.

You could get away with mig but it would look worse.

You should also use a different gas mixture than you would use on the carbon steel. For pipes we would have to purge with nitrogen and use a different mixture of argon and nitrogen.

But if it's a hidden piece you could get away with a bit. Some of the ugliest welds can be structurally sound.

You can learn the skill but tig is the hardest to pickup and master out of the different methods.

If you take the plunge have fun and don't get too frustrated.