I would assume that your home is reasonably cat safe - because of course as a responsible cat owner you will already have made sure of that (e.g. removed poisonous plants). And of course you can always do a quick check before you leave and remove or secure typical traps like shopping bags with handles or boxes with lids that can be pushed open and fall closed. Or restrict access to some rooms entirely, if necessary. Same goes for instructions to the sitter, like to ensure doors (both room and furniture) and windows are closed properly.
Under that premise, having someone come to your home to feed your cats, clean the litter box etc. would in my opinion be a much better choice than a cat hotel.
I have myself been cat sitting a few times, including very shy cats. An experienced sitter will notice if something is amiss on a large scale, e.g. if the cats refused to eat. The he cats being wary of strangers isn’t necessarily a problem - a sitter waiting quietly in some unobtrusive spot may still be able to at least see them, on their way to the food bowl or so, and thus ascertain that everything is well, or well enough considering the circumstances.
The stress caused by your absence and a stranger coming to your home is less than being dragged from their home and being “abandoned” in a completely strange place. Note that your cats have no idea of what’s suddenly going on and no concept of “temporary holidays” - they are suddenly somewhere strange and scary, and without you. And if they are not used to strangers (as you write), the personnel at the cat hotel won’t be able to console them or play/cuddle with them.
If you have a bit of a head start before leaving, you could also try to introduce the sitter to your cats well beforehand - simply by them being around every now and then and possibly feeding them while you are still present. But in a pinch, I would get a sitter and leave.