You can have the best wallet in the world and not be private because you've not been using a private cryptocurrency. There's no amount of wallet privacy features that hides the fact that a certain address holds a certain amount or that a certain transaction has been taken place on a certain point in time.
The only cryptocurrency (that I know of) that has reliably granted these guarantees is Monero, so I'd recommend to use that if what you desire is utmost privacy. However, Monero isn't known to be a good investment, it's a good currency (as far as I am concerned), so you might not want to hold significant amounts of money in form of Monero.

That being said, you usually only require the wallet vendor software to install apps on and update the firmware of a hardware wallet. After that you can use your hardware wallet with a compatible software of your choosing.

You can also use a paper wallet of some kind (I think there are even some metal ones, but I don't know how you etch your seed words into them or how else they might work). You'd usually want to use some form of encryption on those though and then you got to store a secure key somewhere or rely on your brain to memorize an insecure one. Both aren't really superior to just using a encrypted wallet file on one or more storage medias. Technically you could even apply something like Shamir's Secret Sharing to make a M-out-of-N backup (basically multisig, but applyable to all kinds of things).

Personally I don't think there's a perfect solution here. You have to die one death or another.