My 2 cents.
If I read the picture correctly, the faucets can be accessed from either side? If so, they're probably OK. I think people would adjust fast.
I agree w/ JR, you'd probably want flow control faucets here, especially given that you may not get the cooling issue figured out perfectly.
Since it's a remodel, will the wall be opened up? If so,you can line it with 2" foam board and create a chase through which you can push cold air. PVC pipe might work as well. Whatever, you need to insulate the lines and cold air inside.
If you're willing to put a "box" on the wall, you could run 3" pvc pipe up from the refrigerator with the lines in it, into the box surface-mounted to the wall, have that be insulated probably w/ 1" foam board, then allow the air to return down to the refrigerator with a return pipe or line.
The bigger concern I'd have is how you're going to get the lines out of the refrigerator and up to the taps. Most small refrigerators have the coils in the sides, so you'd have to come out the top. You'd also want to consider whether the refrigerator would work well, given that it would be covered up. There wouldn't be much place for the heat from the sides to go.