Excellent idea! I would then cut a slot in the wood, reaching the hole, so you could squeeze the wood around the lens. Much like a ring spanner or filter wrench.
If you can make the hole so that the lens *just* fits in (I use a lathe), there's no need (or room) to squeeze the wood. The object is to swell the wood fibers with water and create friction around the entire circumference, rather than have one area receive more compression than another. Done right, you'll have to carefully cut the piece to get it off the lens.
Micro-Tools sells a wrench, called a FlexiClamp, which is basically a thick sheet of copper with a hole cut in one end and a slot running the length of the sheet. Squeezing the slot causes the hole to decrease in size and thus squeeze the lens more or less evenly from all angles.
If a step closer to absolute zero is really necessary, a grocery store near me now sells dry ice (CO2).
Let's not go to liquid nitrogen...might crack something if rates of thermal expansion (reversed) are too different.
I think the smarter clamp/grip methods are the way to go. Archaeologists find lots of tools showing how smart our predecessors were without tool catalogs, but they've never found a refrigerator. Don't quote me on this.