Should I wash my face with water after applying facial hair removers?

I have used some brands for facial hair removing, however, my skin got a bit darkened these days, and I have stopped using those facial hair removal creams for some time now. I want to know if there is some facial hair removers cream, or lotion, or whatever, that could safely remove facial hair, and would not leave any irritation. I would also like to know if I should wash my face with water once I wipe my face after applying any facial hair removers. Please suggest!