The success of weld repairs on any metal is totally dependent on 1) material, 2) process, and 3) post weld treatment. If you know precisely what the original axle characteristics are, then go for it. Otherwise.... If it were me I'd call Dr. Diff and just chat for a while.
But I am assuming the OP's solution has little symmetry in the suggested process, and even with post weld HT, it is unlikely the he has built in for unaccounted potential stress risers, because of the location, different metals, grain structure, etc. The fact the wheel constantly, in use, loads and unloads the welded area unevenly, is a prime candidate for eventual fatigue induced failure.
The post weld HT is on a one off an educated guess if everyone knows what they are doing.
Regardless, no matter what the OP does, there is IMO, less then a 50% it will fail, but I would not do it.
