If the stainless steel low chromium was cold drawn and had an elongation of some 6 to 10 percent max it would not be a problem
the standard you are looking for is BS6323 Part 6 but it cannot be in the annealed condition grade 410 and 431 would be my pick.
Some of the new grades of duplex and super duplex stainless steels are right up there but its just so expensive, i can tell you what grade etc and the standards but you cannot buy it in small enough quantities in the condition you need unless we buy a mill run Ha Ha
Yes stay away from 316 303 etc as the high chromium is an issue for fatigue cracking
buy the way hydraulic drawn tubing is to soft think plasticine
Good luck with it mate Bruce