I don't know which Stevens you want to weld, but all of them that I have dealt with were cast and I doubt that you will find a good match in a tig rod; also, all my attempts at welding the receivers and levers have failed miserably. Let us know how you come out. Good luck!

Will

Something about welding cast with a tig torch, it may develop hard spots that can not be taken away with annealing. I have used cast iron rod ( Ox/Acc) on Stevens with good results.

Thanks for the input. I have been tig welding for the last  40 years in the marine field. Cast iron has always been a challenge. Never know what alloy you have. I have used  the Ni rod for cast iron, works sometimes , sometimes  not.  Have used inconell 82 wire, silicone bronze wire, even silfos 15 and 45. Problem is in this case got to have color match for  bluing. Think I will look at Bownells at wire  that is made or gun repair. Would like to use tig because of the control of the puddle. Sort of afraid of the gas weld because of potential warpage. Does anyon know wha alloy the 44 is? ....again,   
Thanks for the input.... Larry.

I've used plain MIG wire for TIG on a low wall action. Probably ER70S6. Blues just fine. If the action is cast I suspect you are out of luck but then I'm no expert. If the action is just 'plain' steel then either the TIG or the laser technique shown on the forum a while back should do fine. 
If it is really cast then maybe the only workable approach is to surface grind to try to get under the pitting. Certainly not the best approach to trying to restore something that was mistreated. 

Maybe you want to try a test weld on the underside of the tang. 

I wish you luck.