Before I go on to giving my answer, let me please say there is no Right answer or One True answer to this question. Each tarot reader might have a different opinion and it really is all about you and what you are comfortable with.
I have no issue with letting a client touch my cards. I've even had clients ask if they can go through my cards ot look at the images on a certain deck they are drawn to and let them. I don't feel it has a damaging effect and I usually cleanse my cards, thank them, and give them care between events anyways so I don't feel I'm bringing a jangle of energy home or from event to event to event.
You can always choose who you want to read the cards for. I talk about this in my blog post on reading for people you don't resonate with.
That being said, if you still would like to go on with reading for someone who's energy you don't feel comfortable with, by all means, shuffle, cut, and deal the cards yourself. Most clients won't know the difference. If they do ask why they aren't cutting the deck themselves, just say that you felt moved to do so or were intuitively guided. You don't have to make them feel uncomfortable by stating you don't like their energy.
If someone does touch your deck and you don't like it or feel the need to cleanse your cards, there are many ways you can do so - I discuss them here.
If you are at an event or party, the easiest way is to shuffle the cards continuously with the intention of dispersing the energies on them. Otherwise, you can be as elaborate or as simple in the cleansing process as you like. This is also why I usually if not always have a cleansing stone like clear quartz or selenite near at hand for space clearing.
Still other clients have 2 decks - 1 they read for clients and allow or don't mind when they are touched and 1 for themselves that no one touches but them to keep the bond strong.
I used to ask my clients to shuffle the cards - I stopped doing that when 2/3rds of my clients turned out to be uncomfortable with it as they felt they weren't good at shuffling or had a hard time with 78 cards that were a lil bigger than a standard 52 card playing deck. I still have my clients, when in person, cut the deck because I think it draws them further into the experience and the connection between them, their question, the cards, and me can only benefit from it in my mind.
Like I said before, when it comes to this question, it all depends on the reader and their personal beliefs.