I haven't tried stitching with wire yet but I know when I make gumpaste flowers for cakes I use wire as thin as 33g and as thick as 18 - 20g. When getting a kink in the thinner wires I used one of my plastic or wood modeling tools to "roll" the kink out. Usually worked very well for this.
JC Javelle ~ I also used to be a welder - stick, MIG, TIG, gas - I've used some TIG wire that would be thin enough but I've never seen/used any MIG wire that thin. We always TIG welded all of the real thin stuff.
Something else to use my flower wire for