@010rusty and
@Al e Cat Dabra,
My only personal issue with that is that I hate shuffling the cards right after having them return a card, or In the middle of an effect without a reason other than to mix them up because we just lost there card. I've found that if I were to say (or my actions were to visually say) "ok let me just shuffle up the deck", the spectators are much more suspicious of me, and will then want to shuffle themselves, where as if I simply go on with the trick, they never have that opportunity. It's probably because from the spectators Point of View, the card was already lost when you put it in the deck.
@010rusty, A variation of your method which I actually do use a lot and may actually be cleaner (at least, in my opinion). Do a pass, then use the top card (their card) to gesture to the deck (with the back of the card facing them of course) saying something about their card being lost in this deck (usually, I would ribbon spread the cards if I have a table, or fan them out, and use their card to gesture, eliminating any chance of them seeing there card), and then do a top change, cleanly dropping the new card on top of the old one afterwards. This provides me both a reason for doing what I did, as well as the off beat to do the switch. Plus I don't have to shuffle the cards

If you absolutely must shuffle the cards, do a false shuffle, or one that maintains the top stock, here, because now your excuse is "I have seen the cards, so I must shuffle", but don't say anything about shuffling.
@Al e Cat Dabra Why not get a break under the bottom card in the stock in your right hand, drop the one first, then jog out all the cards after that, allowing your double undercut to directly control the card to the second position? Or why not do a pass after dropping the one card?
Again, this is just my personal view point, if it feels like I'm criticizing you (which I hope it doesn't, because I'm trying not to), just take it as constructive criticism