As NormK has said drill out the weld that is there, take the complete axle off the mower lay the axle on a flat surface and do the weld.
One thing to do is to drill out the weld that is there with a drill size that is large, but not large enough to allow the axle to come through,say 12mm if the shaft is 16mm this makes it a bit easier to weld.
Once you have welded it I would suggest drilling through the outer and the axle and fit a roll pin through the lot, do this on both sides, as if one side has failed sure as the sun rises tomorrow the other will probably fail.
Putting the roll pin in will help take the stress out of what is already a weak design fault, not only have they turned the shaft down but they then reduce the effective diameter by cutting a thread onto it.
If you don't have the skill with welding this is not a big job for someone who can weld, probably a couple of minutes.
Beech.
