Why?
What about grub screws?
Or even JB weld if you really don't want the holes. You could fill the holes that way and not affect the integrity of the metal due to heat and get a nice level finish.
Just my 2c
F**k JB Weld! Crappy five minute epoxy with a bunch of metal powder added in.
It's firstly, a .22 Pump action rifle, and not liable to blow up at random. Second, anything done to it by heating and cooling, is going to far exceed the strength of a 3/16ths of an inch hole, being there.
Get it TIG welded. Or, if you can find a dab hand at it, Oxy-Acet. Mild steel filler wire, coat hangers will likely do inna pinch, but anyways....
There is a possibility that there will always be a little bit visible in the area of the weld, due to the bluing not matching exactly.
Another viable method, is to fit in some threaded plugs, which are trimmed just a tiny bit above the surface of the action. Then peen the ends over, using lots of 'small' strikes of a hammer, and likely, a punch, so as to avoid denting the action.
The idea is that many small light strikes causes the near end of the plug to expand to fill the top of the hole, without leaving any visible gaps.
The plugs are then worked off flush, and the area touched up.
If well done, these can provide an almost invisible repair too. But they can not be drilled and tapped at a later date, if that was possibly an option, while a weld repair can.