Been there, done that, it's far more worrisome when you have to show them how to put the harness on and then have them test that it's tight enough.
And like you said, you really don't want to touch them.
The simple solutions is to show them how you take your harness off, and have them mirror your actions and go through the steps slowly.
I will point to what they need to do, or if they have someone else with them, who they are more comfortable with like a sibling or parent, have them assist the person.
outdoors.stackexchange.com/users/8794/Charlie Brumbaugh
I don't have anything to add for the specific requirement of removing ones harness, the live-demonstration/mirroring recommendations in other answers should do just fine.
I want to address a slightly more general point: [...] without touching them It should become blatantly clear from what follows (and shouldn't be a debatable point anyway), but to be safe: If anyone does not want to get touched, you don't.
However invading the personal space of your climbing partner is not optional .
Before climbing you always do a proper partner check and that involves checking manually that biners are locked, harness sits tight, ...
That's even true for top-roping.
If we are talking about leading (high first bolts) or bouldering, the need for touch becomes even more blatant due to spotting.
If the climbers hip gets above your shoulder height, the point of initial contact in case of a fall is the hip.
Is this potentially awkward?
Sure.
Is it better than falling directly on your tailbone from ~2m?
I think so.
The important point is to explain early and clearly
why and in what situation it is necessary to touch or get into the others personal space.
It needs to be abundantly clear that it is a safety necessity.
Then ask individually when the situation comes up .
The consequence is, that if someone legitimately feels uncomfortable about it, you either need to get someone else to do the partner check, or in case of spotting, you just can't do the climb.
In general if you can't bear your belayer to touch your harness and hold your behind/
back/
...
in case of a fall while spotting, you might want to rethink whether you want those persons to belay you - they do hold your live in their hands when doing that.
outdoors.stackexchange.com/users/3602/imsodin
It is not really about instructing people how to take the harness off, but rather about respecting the personal space of clients.
I suggest having an instructor demonstrate the steps to take off the harness when the harness is put on and again when the client is about to remove the harness.
This requires having a spare harness, but just like on the airplane, the instructor probably does not need to be wearing the harness and instead only needs to show the steps.
After demonstrating how to remove the harness, the instructor can then tell clients that if they are having problems, they can ask for help from either a friend or the instructor.
If the instructor is asked to help, he should explain the steps again and where he is going to touch the individual and then confirm that the client is okay with that.
For sit harnesses, the touching should be limited to the waist as most harnesses allow people to step out of the leg loops without loosening them.
For chest harnesses, there may be a buckle at the sternum strap, but most I have seen have either a carabiner or a rope, neither of which should involve physical contact.
outdoors.stackexchange.com/users/5836/StrongBad
It would take more time
but when they are dry at the top have them remove the harness on their own for practice.
Tell them when they get to the bottom they should remove the harness when given the signal to do so.
If they need help an instructor is also at the bottom.
outdoors.stackexchange.com/users/6728/paparazzo
When you see them struggling ask for permission to help before touching.
While helping try and maintain a professional distance away.
There is a big difference between getting up close and personal to fiddle with the buckles and doing it at 3/4 armlengths away.
When handling the buckles around the waist and legs you can squat down which is less invading than bending over.
When you need to check the harnesses limit the actual touching to the tie off points on it.
Emphasize in advance why it is important that the harness is checked properly, maybe with a bit of a horror story of what could happen if it's not properly fitted.
outdoors.stackexchange.com/users/15492/ratchet freak
After rappelling near waterfalls, or during the rain,the harness often becomes wet and hard to remove -- particularly for inexperienced people.  How can I instruct someone in how to remove the harness,without touching them?  I have heard people, in particular women participants,(reasonably) complain about their personal space and about bodily contact,when someone else has removed their harness for them.
How to instruct someone how to take off a climbing harness?
outdoors.stackexchange.com
<gear><climbing><harness>
outdoors.stackexchange.com/questions/19088
outdoors.stackexchange.com/users/2303/WedaPashi
The simple solutions is to  show them how you take your harness off, and have them mirror your actions and go through the steps slowly.  When you see them struggling ask for permission to help before touching.  Emphasize in advance why it is important that the harness is checked properly and try to maintain a professional distance when helping. A sibling or parent may be able to assist. Show the person how to do each step, you must respect personal space.
This is important, but you must respect personal space. Show the person how to do this step by step.