Is it safe to publicly expose PBE-protected PGP secret keys?
What I understand from the question, as if you have a Certificate Authority key around. 

Using an air-gapped pc, raspberry pi zero, etc. is a good choice. The important points;


Sign the document in the offline solution, do not carry the key.
You can have more than one air-gapped solution. Extra hardware against failures.
You can keep your old paper around.
Have an extra security against the easy copying from the device




Extream care 

Off-line encryption: In the military, when a message is top secret, the message, firstly, encrypted with an off-line system that has no connection to the network. After the off-line encryption, the message is sent by on-line crypto. The problem is not finished here. 

Tempest Attack: The signal from a pc can be carried by air or the power lines. This requires an expert in this area to filter the machine. So the off-line system and the power lines are filtered.

Covert channel: If an adversary can install a software to your air gapped solution that he can use the heat to transfer the data. Have a mechanism to prevent access to the solution.