What if you create multiple paper wallets and you split the main hoard into smaller chucks and distribute it via a Mixer service from the main hoard to the paper wallets?
This can work well, provided you are smart about it. If you fund 5 wallets (for example) in the same transaction, then obviously they are linked. If you fund 5 brand new wallets with the same amount, with all the transactions in the same block, then that's probably linkable as well. You also have to be careful with depositing exactly 1.024 BTC to ChipMixer and then withdrawing exactly 4x 0.256 BTC chips, for example.
If I sent part of my main stash to ChipMixer over Tor, and then a number of days later sent an amount to one wallet, and then a different number of days later sent a different amount to a different wallet, and then maybe sent a bit more of my main stash to top up whatever I still had in ChipMixer, and then withdrew another different amount, and so on, and donated a few chips along the way, then it becomes near impossible to track.
Once you've done that, then every paper wallet is essentially an anonymous standalone wallet, and cannot be linked to you or any of your other wallets unless you make careless transactions or leak information another way.