I never did it on a 10-22 but there are a lot of stocks available for them. Cabela's has a whole page of them.
Some of them come with sling mounts too.
Buying a whole stock for a 10-22 seem like a very expensive way to go though and I would likely just go with the screw in sling mounts.

I am not sure about the barrel band on them either.
I am just not familiar enough with Ruger 10-22 to comment on that.
However seeing that people do float the barrels on them and make varminter style stocks for them I end up wondering if the barrel band really does anything.
After all they didn't even put a barrel band on the 10-22 Compact model.