Use 1password (or similar) so there is no master password? You can have 2 trusted people be administrators of the 1P account. Then you create a shared vault for anyone who needs access to the master credentials and store them all in said shared vault. You can have multiple vaults with multiple different sets of credentials and access (Ex a vault for HR is going to have different creds and people than a vault for DevO…
Why would you suggest 1password on any other shitty proprietary crap. Use Bitwarden, its Open Source you can self host it inside the company if you want ... and if they every do something (shady) you do not like you can switch to a fork that will instantly pop up as soon as that happens.
What do you think about trying something like, "Good points about using a password manager. I think Bitwarden is better than 1password becuase it: is open source, it can be self hosted, and you could switch to a fork if they get shady."
Because you wouldn't be implicitly calling them ignorant this way, they're more likely to hear your message.