The idea is to create a paper Bitcoin wallet, put bitcoin into it at a Bitcoin ATM, and then redeem it for cash in the future at a second Bitcoin ATM, without using an online wallet that could potentially expose my personal information. Or something like that.
Is that possible?
How do you plan to "redeem" a Bitcoin wallet for cash? This would only be possible if you give the ATM providers access to the private keys, or they created it themselves (and you never owned it, similar to how centralized exchanges work).
To protect your privacy, you can run your own full node and transfer your funds over an airgapped device which never goes online.