It's still a 3rd party.
If you want to use a dead man's switch, then you pretty much have to trust a third party somewhere, since you won't be around to oversee the process yourself. The safest way would probably be to set up a program yourself on a dedicated computer, but you still have to trust the computer doesn't fail, your ISP, it isn't attacked, etc.
The seeds would be on paper with the hardware wallets in an envelope.
If you are going to store the mnemonic phrase in plaintext along with the wallet, then there is hardly any point in having a hardware wallet at all. For a passphrase alone to be secure as a 24 word mnemonic phrase, it needs to be 37 random characters from the 128 character ASCII set, and something this complex should also be backed up on paper.