Given the season, odds are that it's dry skin. And, even if not, oatmeal bath can help with the ouchies of quilling. There are two main ways to accomplish this:
1. You can get regular oatmeal (like the kind you'd eat), put some in a sock, prepare the bath with nice warm water and a washcloth for him to stand on, before putting him in, swish the sock around in the water until it's nice and cloudy, then put him in. You can leave the sock in there during bath time or take it out. Think of it a little bit like a tea bag sitting there in your cup of Earl Grey.
2. You can use colloidal oatmeal that's usually sold in a box of several packets. Put the washcloth in, then sprinkle the oatmeal (about a quarter of a packet) on top of the washcloth, start running the water so it's warm, then start filling the tub. You'll still have to break up some of the oatmeal blobs with your fingers, but less so than if you tried water first, then oatmeal on top.
There's also the Aveeno oatmeal wash (or store brand) that comes out looking a bit like a liquid soap. I don't like that quite as much for dry skin issues. If you look at the ingredients on that... there's waaay more ingredients listed than either the plain oatmeal or colloidal oatmeal.
Whichever you choose, use your free hand or a little cup to scoop up a bit of water and pour it down his back. Keep the water that you're pouring away from his face. And definitely out of his ears. With any luck, he might put his front feet on your fingers so his back is a nice little incline.
I don't rinse afterward. But I do give a nice snuggle. Just let him dry in a blankie/towel/fleece on your belly or in your lap until he's all set. Don't try to use a hair dryer or anything! The oatmeal will help, but don't fool yourself into thinking "oh, I'll just do this every day and problem solved!!" It's more a once a week max type of thing. You can get a little gel cap of flax seed oil and put a few drops on him... I'd aim for maybe a day or so after oatmeal bath time.