Or could I get away with, say, 6 hours in the fridge?
Is it similar to this recipe by Alice Medrich? If so, I have chilled it for a few hours and they are still delicious and didn't spread. They were better the next day after sitting for 24 hours, but the difference wasn't gigantic.
I would stick the dough in ziplock bag removing all of the air, place in an ice water bath and stick the whole thing in the fridge.
Thank you both! I ended up doing the ice-water bath in the fridge--I was able to leave it for ~7 hours, and they turned out perfect.
Great to hear it worked out.
The Ziplock bag in an ice bath works for many things when you want to chill fast, don't want to dilute with water, and don't want to risk freezing (ice crystals forming). Plain old middle school level physics.
Most cookies are pretty high fat- if it's not much more than 1 fat to 2 flour by volume, chances are good you could skip it entirely- certainly 6 hours is more than adequate.
Here's another idea: after making the dough, press/flatten it into a disk (or disks) about twice as thick as you'll eventually roll it out to. It will chill really fast, unlike a ball of dough. It will also be much easier to roll out once chilled, since you'll be starting with dough that's mostly rolled out already.