The factory grips will make it either way. That's one of the nice things about this guns design. You can call it whatever you want unless something in the metal is different then we need pictures to verify your claim Please.
I do not believe S&W ever produced wood cases for the Model 41 so I doubt the case is original. New - never fired is going to be worth more than "almost never fired" so I would get clarification before paying a premium. Never heard of an LH model so please explain.