Just thinking: what would be even more gradual approach? I know a guy who is already scared by the idea of dancing.

I was scared of dancing before I started Salsa dancing. It wasn't easy at the beginning as someone who didn't do any sport beforehand but I managed with time.

As far as non-dancing physical activity goes there martial arts which is scary for other reasons.

I would recommend Western body work systems like Feldenkrais and Alexanders Method over Yoga. Yoga isn't bad as such as such, but there a lot of unquestioned dogma involved. Things are done in a certain way because they are thought to have been done that way 1000 years ago in India.

If he's scared of dancing for social reasons, I would think that the underlying causes of that would have to be addressed. Off the top of my head, this might be a good gradual behavioral approach (but wouldn't address any of the underlying cognitive causes):

1. Pen pal.
2. Do something that involves cooperation in person, but not socializing.
3. Go to a meetup that is like semi-professional and semi-social.
4. Go to a social meetup.
5. Toastmasters.
6. Learn to dance.
7. Initiate small talk in acceptable situations (with the barber, taxi driver, contextual comments to the person sitting next to you).
8. Initiate in a more random way. Ex. Hey, I like your glasses, where'd you get them? Something tells me that you're a <sport> fan - did you see the <home team> game last night?

If his fear is more specific to physical activity, then I agree with you about starting off with something like Yoga. Some other ideas: Racquetball, Running, Ping Pong.