No Problem.
The "slowest" powder I have used for 1 oz has been International Clays, and even then I did not like the performance. In shotguns it performs/has a pressure curve similar to Green Dot, and when I tried it w/1 oz, I had a lot of unburned powder which this powder normally does not do when loaded with 1 1/8oz, and the smell after firing was very acrid, and the same smell you get with inefficient burning. Wad pressure was fine, and hulls held a nice firm crimp.
When I load 1 oz I always used Red Dot, 700x, and from about 10 years ago Clays. (Just Clays, not International or Universal). I think your idea of getting plain Clays for 1 oz is a good choice, at least it has been for me. Good loads can be found right at the Hodgdon website, and is what I use or the Lyman manual. I like to look at the pressure tables given, and don't like any shotgun load to go below 9000 LUPs/psi, and prefer over 10k. Seems when you use loads with 6500 psi or less, the chance of blooper/off sounding rounds happen, especially in very cold weather. Lots of good choices out there, and IMO, a lot better than Unique to drive 1 oz 12 gauge loads. If you ever want to "step it up" a bit, and would like to load nice International style 1 1/8 oz loads, might give "International Clays" a try. It produces very clean, very consistent ammo, that makes it very easy to get 1270 fps loads if you should want them.
Good luck!