Something is totally scarey about all of this. You said pinion bearing at first which can't be installed unless you do a trial and error depth setup so it properly meshes with the ring gear, which must be shimmed to obtain the right backlash. It's a tricky procedure.
Now it sounds like you're talking axleshaft bearings...
... what ring to you plan to weld into place?
The bearing retainer ring? That isn't welded into place, that is pressed into place after the axle retainer, seal, and bearing have been installed.
To put it mildly, I'm very concerned over the questionable outcome of all of this.