What can I use on the Arizona hot rocks for my dogs

can you make a small area with just dirt/sand. I don't see how anything could make rocks comfortable for a little dog to walk on.

fabric sails tethered to the ground and poles to create shade for the area, and maybe replace the rocks with something like rubber mulch that would be less hard on the dogs pads

Can the rocks be removed to clear a pathway?

Why not clear back the rocks about a foot (a little more if need be) to make a winding path filled with sand leading to a nice sandy area for he can do his business. If he will learn to use that space, you only have that area to clean up and lime!

short term.....hose it down to cool it before he goes out.

You are a good doggy parent! I agree with others that recommend moving some of the rocks to make a path. Adding astroturf to the path could also work.

How about making him some shade? Here in Ohio, I put a table outside for my dogs so they could pee outside under it and avoid walking on the snow. You could use the same concept. Coleman sells a pad for dogs to sit on that is cooling. You can get it on Amazon. (I have used it myself for hot flashes in the night. Works great). Its washable. Even if you put a trail of these pads on the ground for the dog to walk on to the pee area....it could help.