FWIW, If it were me in you place (and I'm glad it's not), I would grind it out real good, preheat and reweld it with some 309 or similar (308). Of course, I never said to do that. I'm just thinking out loud...

Hello grizzzly, you are fighting a battle here that is going to be hard to win due the constrictions of the application. The shaft is hard, maybe only case-hardened, but hard non the less. the sprocket is similarly a hardened material. In a perfect world you could remove the shaft, anneal it and the sprocket, and then weld them and harden them after the welding has been completed and possibly end up with a repair that would have some longevity. You already know that that isn't possible in this scenario. Having to concern yourself with the seal that is located directly behind the sprocket is a large limiting factor. Since you need to keep the shaft cool during this repair you would probably be better served by using a GMAW process to perform the welding. Not quite the penetration that GTAW could provide, but certainly less chance of having issues with burning things up either. A choice of using a stainless filler as was eluded to by Superflux is likely a decent choice considering that the nickel might provide some give for the stresses that will manifest while everything is cooling with these hardened materials. Peening the weld deposits immediately after applying the weld might help also.
     You mentioned arc-blow, when you are welding on this particular area of the motor you should really try to attach your ground directly to the sprocket. If you are grounding elsewhere on the motor you may run the risk of arcing the bearings in the engine or transmission. I would also disconnect the battery and possibly the ignition module before performing any welding. If you have already done welding without causing any issues with the motor you may have been lucky, I don't know whether I would push that luck.
     One more thought occured to me as I was writing this, using the GTAW process and silicon bronze filler metal might be a better choice for filler as this would essentially be considered more of brazing process instead of a welding process and possibly limit the possibility of cracking in the finished condition.
     Superflux also spoke of safety considerations. Not correctly addressing this problem could lead to a failure that could cause you personal injury. If for some reason this sprocket repair fails and jams the chain up you could be in for a really wild ride, so consider that you are doing this sort of thing at your own risk.
     I personally believe you would better serve yourself by biting the bullet so to speak and going ahead and doing the teardown and repair as it should be done and replacing the shaft and sprocket. It is, however, your choice. I have been in similar positions myself and have cheated the reaper at times, but not everyone is lucky like that. Best regards, Allan

With regard to the arc blow, You might try putting a thick steel plate between the alternator and the area You are welding. As Allan mentioned, ground to the sprocket or shaft, more for the sake of not arcing the bearing surfaces, but it should help with the arc blow too.