Thank you all very much for your ideas!
Several people wanted to know more about the end-game. I want a scheme that makes the water clean enough to dispose of, and the oil sufficiently water-free to drop it off with my other waste oil at the local auto parts store without giving them more than a nominal amount of water with it. They're always OK with a little water, but don't like it when there's a lot.
Snowman's pan-in-the-sunlight sounds good, but it rains here during the summer basically every day and I am sure to get nailed before the water all evaporates. Other locales may find this works perfectly.
Sea Farmer's turkey-fat-separator also sounds interesting, but my wife has a smaller version and I was noticing over the holidays that meat fat doesn't mix with the water at all. The oil I'm dealing with is partly emulsified; there are lots of little globs of it. I tried separating it with a siphon using 1/4" tubing, thinking that the liquid flow rate would be so small that it wouldn't agitate the bucket and I could get good separation. Didn't really work: too many little oil globs.
David Scott's paper towels certainly would work and is the simplest way, but as he notes the oil then heads to the trash. If it was really just this one quart of oil, I guess I could grin and bear it, but I'd like to have a method in my "toolbox" to separate and recycle the oil for future use.
cmccull166's suggestion to call Shell is excellent, and come Monday morning I'm going to talk to someone in their customer service dept. Also, the absorbing pads re-purposed as bonfire ignition aids is sort of recycling, but...
I want to check with Shell, but Trevj's idea of adding some heat and boiling off the water has me thinking pretty hard. All these oils have boiling points at least several hundred degrees F above the boiling point of water. If I kept the pot at 212 degF, I'm sure some of the oil would evaporate but not at anything close to the rate that the water would. I want to look into this a little more.
Thank you all again very much!
Best,
Dave