once you sign a txn it's just a string of hex characters that somehow need to be broadcasted to the bitcoin network. it can be done from everywhere, by anyone. good wallet hardware/software should give you the ability to just get the string of signed txn in hex format

https://www.blockchain.com/explorer/assets/btc/broadcast-transaction 

 Right. But if you are fully pre-signing a tx that spends your entire cold stack… you need to protect that hex so it doesn’t accidentally get broadcast 😂 

 let's say it's not a good idea to keep it as a text file on your desktop 

 Yes, but if tx get broadcast in the network, the funds will be sent to a new wallet, just it. The original owner alredy have the keys.