1W of green would require a 5W pump diode, which needs just over 6 A to operate normally - way above any reccomended current draw from any 18650 if you want them to live over 1 hour. Or at least not explode agressively.
Sorry, it's not possible.
Your best bet is to have 2 or 3 W IR c-mount in there and have a very powerful IR burner.
Visibility would obviously be 445nm 1W, perhaps even ran at 1.8-1.9 A and have just over 1.5W out of it.
But for a green, this is as best as it gets for the money:
High power 400mW green laser module/IR filtered [OLHGLM400] - $380.00 : Welcome to O-Like.com, Your source for laser products
Bill bought one of those and it does 550mW peak I think, just over 500mW average or something. See his channel on youtube "billg519" , same username here.
You can also ask him about powerful IR builds, since the guy does have 4W IR in a handheld host. Uses some big*ss 2x 26500 or something lithium ions.