~snip~
if the seed and the password are kept secret, anyone stealing the offline machine still can't steal the bitcoins.
I think they can still get your bitcoin out from your encrypted wallet with a password even without the seed or password.
If you don't know about the tool called
BTCrecovery they can brute-force the wallet file to take the password.
if all you have is a paper wallet, how do you sign transactions on the online machine?
You have a point here.
Anyway, about your question, I think you don't need to update the OS if the Electrum installer works without any issue after installation. Just leave it as it is. But I think for Windows 10 OS some people experience some issues when running Electrum. So I suggest if you are going to make an offline cold storage use ubuntu OS instead.