I used a firm local to me Amac Engineering in Northallerton North Yorkshire to repair the cavitation plate on my outboard. Brilliant job & very reasonable pricing. They specialise in welding car cylinder heads etc so it's obviously possible to avoid distortion etc but you'd definitely have to strip the gear box of all internals & seals before you start.
I'm not suggesting that you use Amac but there may well be similar firms in your area if you google your local towns. I did all the prep & finishing on mine to keep costs down.