I put mine in the shower today. He loves it. Especially if he is coming to the end of his shed cycle. He actually ran to the water and just sat under it for about 5 mins then moved a little distance and just let it run all over him.
The only issue that might arise is once you shut the water off. The temperature drops pretty quickly and your cham may get a little chilly. Try and get him back into the cage at the earliest possible time. Clyde did his satellite manuever once I had him back in his cage. He wanted to warm up a bit under his lights after his shower.
And a second issue....be mindful of how big your water heater is. I get about 30mins of warm water before it runs cold. Since its winter, that water will be ultra cold.