I do not know any wallet for making PSBT but you can use some open source wallet with multiple coin support offline and have the master public key on a watch-only wallet.
I know Unstoppable wallet supports that. Maybe you can try it.
Yes, a first step would be to list software wallets that do accept a master public key. I wasn't aware that Unstoppable wallet supports that. That being said, i read on their website that Unstoppable is for mobile device. I would prefer a software running on Ubuntu desktop OS.
Maybe you can have multiple of the wallet offline so you can just select on one for making transaction if there is any need which will then become online wallet.
Some people just use the method to hold their coins and not spend from it at all.
What is the purpose of having multiple of the wallet offline and selecting one for transaction vs having multiple offline wallet?
Cheers