0707
The fillet weld repair that you contemplate will have much, much less resistance to fatigue failure than the original shaft; furthermore, fatigue life cannot be quantified. Welding residual stress is additive to the imposed design loads and the fillet weld design presents a mechanical notch. Any such repair should be considered highly temporary at best. The shaft must be rebalanced as well.
A mechanically connected sleeve repair or other mechanical connection could be designed with calculations providing some basis for remaining fatigue life. Again, I would consider such a repair to be temporary but at least predictable. Note, the problems with rebalancing the shaft.
Repairing the shaft with a full penetration weld repair, machining to size and fully heat treating to the original temper will provide a better solution, but again, full restoration of fatigue life will not occur. The weld repair will still be the weak link.
Replacement is your best bet for a long term fix.