I wouldn’t use Kwik Fit either.
When a thought I needed a new tyre last year, I did some research on tyre places in my area to find those with good reviews (I know, that not all of the reviews may be genuine, so they need to be treated with a pinch of salt). I also looked on Black Circles website at reviews of the tyre fitting places classified as Premier Garages, plus I did a separate search for customer reviews on those independent Premier Garages. I found one that was reasonably close to me and they were very good. If they have a touchless tyre changing machine, even better, as that should minimise the risk of any damage being caused to your wheel.
I’d recommend that whoever you go to, you make sure your wheels are clean and you get the tyre fitting place to agree the condition of the wheels before they start work (take photos of them while on their premises if you feel need to). Check the wheel with the problem tyre on it over carefully before you leave their premises too. That way, if they were to damage the wheel when they remove / refit the tyre, then it’d very difficult for them to deny having caused the damage.
Overkill? Some would say so, but I’ve read of enough cases on forums over the years of owners alloys being damaged by careless or inexperienced tyre fitters, and if they know you care about your wheels, hopefully they will too.