As with a lot of the craft its about following your intuition. What do you think would help you bond best with your deck? Its all a personal preference with some saying it has to be very ritualistic, and others saying don’t worry about it at all. I’ve never really cleansed new decks, because I don’t feel the need to (others do, and thats totally fine!). But I do things that help me bond better with my decks, which I find helps me work better with them.
One example is I keep my personal deck my nightstand beside my bed. Another deck I carry with me always. If leaving it outside during the new moon, which sounds like a fantastic ritual, does it for you go for it!
Caveat, again this is all down to personal taste. I do let others handle certain decks, and for those I do feel a compulsion to shuffle them extra good after the session is done. So that’s my little cleansing in a way.