They are truly disgusting, I remember my first encounter with them well so entirely sympathise with how you feel OP.
Sadly, this time of year means you will encounter them multiple times.
The mere thought of going near the critters used to make me feel like vomiting but figured it was something i had to learn to deal with as hate the stress of taking kitty to vet even more than the tick(s)
Best thing i've found is a tick pen - looks like a pen, you click the end & a plastic lassoo comes out of the end.
Push lassoo around tick, quick twist, put tick on toilet paper/kitchen roll & flush down toilet.
Don't do what i did & listen to internet search advice & try to squash the tick or burn the buggers, the liquid that comes out of them has to be seen to be believed & is not healthy for humans to touch to put it mildly.
I've tried various tick hooks they sell in pet shops & vet's but they are a pain to use plus you need a different size hook for small/big/medium critters.
Doesn't matter what size with the pen as the lassoo adjusts automatically iyswim?
Found mine in a local farm shop, having lost the first one I had.
I"ll have a look for a link for online order in a minute.
Not particulary helpful to you right now i realise but dealing with the critters does get easier with practice & now its just a routine 'oh, its that time of year again' job.
Hard to believe given the level of revulsion i used to feel, amazing what an aversion to a vet trip can do :)
If you can't face going near it til you can get the vet to take it off then there's no immediate danger to you or your cat. If the tick is really swollen & big then best to keep kitty off your bed for the night in case it drops off (eventually they just let go when full enough with blood)
Revolting, i know, sorry :(