I've not searched, but i've not seen what steel the slide is made from. The 308 filler would almost certainly work, as it's very flexible about mixing, but, it will not blue, or likely take phosphate, so, it woll depend on your plans for refinishing.
It is always possible there will be a hard area around the edge, you may need to mill, using carbide tools, if only going half the hole. I'd start undersize, so if it wanders a bit, you can true it back in.
Brownells sells a tig filler suitable for tool steel slides and such, blues well, comes in a smaller quantity than weld supply shops.
Heat is based a lot on thickness, steel or stainless is not widely different.
You will affect the temper in the immediate area, but the muzzle isn't under a lot of stress. The muzzle barrel opening sees wear, but if you're quick, should be OK.
Welding prior to beveling would be preferred.
ETA: looking again, almost looks like a stainless slide. If so, definitely the 308 would work, or 309.