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?
You just want to spend part of the coin in a way your private key is not imported on an online device or probably because you still want to be making use of the paper wallet and you want to spend some coins from it and you do not want the private key online but to remain completely offline, you can follow any of this guide:
You can learn how to setup an
Electrum cold storage and watch-only wallet which can be used for it.
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). This doesn't sound like an outlet which an ATM provider would want to create.
Exactly, which is not possible, any ATM that demands for private key is even for scammers and this has never happened before because ATM are not easily setup. Seed phrase and private key must be private and reamin known to only the owner.
To protect your privacy, you can run your own full node and transfer your funds over an airgapped device which never goes online.
Running full node or pruned node on Tor can help in privacy but this is not about privacy, it is about how to spend bitcoin in a way the private keys does not going online.