I bought an inexpensive
4-deck card shuffler from Amazon a while back, and it does fairly well on my sleeveless cards. I have all the regular Munchkin stuff except CWBH and it can handle all the Treasures at once, but the Doors have to be shuffled in two batches.
If your cards are super new they might not shuffle as well, but after a few games some of the new gets worn off and the shuffler shuffles them easier.
Occasionally a card or two gets flipped around (so a deck face-down has a face-up card or two in it). I don't worry about them - my rule is if a face-up card comes to the top it's immediately moved to the top of the discards. If a player wanted it they can play a card that lets them go through the discards. The exception is if drawing multiple cards (like epic Door-kicking or multiple Treasure from kills) they can still take it as long as it wasn't the top card.