Briggs made both overhead valve and L-head 190 cc engines.
I used to build automotive heads for a living. The answer to your question is an unknown. Sometimes the peening will hold a slightly loose seat depending on how much crush you can get on it with a peen, and how much aluminum you have to work with to hold it in. It is not the preferred method but a mower engine is too inexpensive to go thru the process unless you own the machine shop or your brother does, etc.. However the seat has already fallen out, which sort of implies two things, (1) the seat is really loose, and (2) that the engine got really hot at one time (which has to be dealt with if it is still happening). The danger of a loose seat is it drops again, the valve bends, which destroy the guide and the valve. The valve head then rattles around the combustion chamber and destroys the piston and cylinder walls.
Is this an overhead valve engine 190cc , or 190cc engine where the valves are in the block? If it is overhead, buy a new head now before the seat comes loose again and destroys the engine.