The cat isnt shy, it is nervous. Shy is something we humans are, cats are nervous and that why it pees on you. To make sure you let go and it can run away again.

If he got used to it being in a specific place, he may not have an easy time adjusting. In my experience, most cats have a very strong dislike of changes in their environment or routines. It's not impossible to get him adjusted, but it might not be the most fun thing in the world, especially if he's nervous already.

Is there any way you can put the litter box back where it was? A cat, especially nervous ones not used to their surroundings, tend to like routine. Honestly, nearly all cats like some sort of routine. You may end up with the problem of the kitty peeing in the place where the litter box used to be. I'd suggest maybe gently urging the cat towards the new litter room until it feels adjusted enough to go in and out by itself. I know it's a pain OP, but it's better than cat pee everywhere

cats aren't shy animals, just picky as to who they like or accept and need time to get used to new people or surroundings, try Bach plant extracts, cat mint or calming drops..usually helps. good luck with your new furbaby OP

Look at me. LOOK at me. You are the litter box now.

Mammals don't like having their shit moved around. It oisses them off. Now you know.

The cat probably would have found it on its own...still you might have been better off leaving it where it was...

LOL! My oldest has a tendency to do that when he freaks out. At least the cat peed instead of fighting back!

could've been worse... could've been moving your pet skunk's litter box

So you knew the cat didn't like being held stop picked it up? I'm not saying YDI but that could have been thought out a little more, no?