Hi Glenmc
It’s quite refreshing that cats on this occasion aren’t the problem. More often people are trying to find ways to prevent them eating the hedgehogs’ food!
If the hog is a male he might move on after a few days anyway (they do tend to move nests fairly often in the Summer), but you could try getting/building a hog house and he might decide to move in there instead. But it would really need to be a case of him choosing. If it’s a female hog planning on producing young in the cat shelter, you should do your best not to disturb her.
Of course I have no idea how large this cat shelter is, so no idea how silly it might sound suggesting maybe another cat shelter?! Hogs can be very perverse at times and turn their noses up at a lovely hog house, only to nest under a shed.
Here is some info. about hog houses:
https://www.hedgehogstreet.org/help-hedgehogs/hedgehog-homes/
