When I deal, (not in a self-dealt game) I will bring in the folds to the muck and I will mix it up as I am dealing and waiting on players to make action. At the end of the hand just below the board, I have 3 cards (burns) a stub and the muck. I flip over the board with the winning hand and then wash it all together, nothing super crazy, just enough to reorder all the cards, as I ball the cards up I'll take cards off the bottom and top and slide them to the bottom of the deck, then straighten them, next up riffle riffle box riffle cut and pitch...
Most of the time I will have a shuffletech so I don't actually hand shuffle, and I'll hit 7 on it so we get more randomized decks