I have 8x10ish sheets of 1/32 and 1/40something wood veneer in a few different tree flavours. I know nothing about wood, so I can’t identify any of them, which isn’t very helpful, but some of them are definitely flexible enough for this kind of project without soaking. Assuming it could be glued along the edge and not creased.
Some of them are more brittle along the grain lines, but even those I think are still flexible enough as long as you aren’t trying to flex the wood in the wrong direction. I don’t know if I’m making any sense. Horrifically, this is me after learning a lot about wood from the forums. Lol.