By military bolt handles, do you perhaps mean older era military BA rifles that you are sporterizing? If that is the case, knowing the metallurgy of the bolt(s) in question is an absolute must for a proper TIG welding process, FYI.. RWTF
When I had easy access to a TIG welder at work, I welded bolt handles on a few bolts. Two were 98 Mausers and the other was a Siamese Mauser. I made a bolt welding jig like the one sold by Brownells to hold the new handle in the correct position. I also used the 3.5% nickel steel rod sold by Brownells. It worked very well, and the process isn't all that difficult.
I did wrap the forward part of the bolt in a wet cloth to keep welding heat from the bolt lugs. My bevels were ground to permit near 100% penetration to insure a weld job that wouldn't ever fail. And I also coated the internal threads for the bolt shroud with PBC anti-scale compound. If I were going to have someone else weld one for me, I would be very specific about the protrusion of the stub, and the angle of the new bolt handle, simply because I have seen some that just weren't done right, to my eyes.
I just missed a screaming deal on a nice Hobart TIG welder at a Car Parts Swap Meet I went to several weeks ago. Still kicking myself for not getting to that vendor about two minutes sooner.