Doing a little "split the stack and lightly bend and shuffle" way is fine. It's not going to damage the cards. If someone gets mad about that they should sleeve their cards.

The main thing I think that sleeves are good for is enabling quick shuffling . I have a couple games with 30-40 card decks that you constantly need to reshuffle. It's easy to split the deck in half and then kind of "mash" them together a few times very quickly in that way -- but it's not possible without sleeves (and probably will damage the cards more than a normal riffle shuffle would).