It just doesn't work that way. The wallet has a secret which can be used to sign a transaction to spend the balance. It doesn't need to be connected to do this.

It just doesn't work that way. The wallet has a secret which can be used to sign a transaction to spend the balance. It doesn't need to be connected to do this. The transaction is a serialized piece of data which can be broadcast to the network. The size varies depending on certain factors, but it's usually about 250 bytes. Electrum can create this transaction and show you a hex dump of it which you could copy off and submit to the network from a different system that is online. An attacker who controls the online system would be unable to modify the transaction. With more than $10M at stake it is prudent to do that, just like it would be best to use an armored truck to move $10M in cash.