I'm not sure what you mean here, a wallet is considered as cold storage as long as It's not connected to the internet.
Electrum has the ability to sign transactions on an offline machine and later broadcast them from an online machine, meaning that the online machine never "sees" the private key (
link). I am trying to figure out if there are any advantages to using this method for a one-time transaction (vs. signing and broadcasting from the same online machine).
So, assuming that you're just holding for long term (as you didn't give details), here what I suggest to do: Either buy a hardware wallet like I already said above or use another paper wallet by encrypting the private keys using a password. As on how you transfer the funds, just install Electrum on Ubuntu like you planned to do, keep it connected to the internet and sweep the funds there and then send them wherever you want to.
Holding for long term, but not entirely sure if I want a HW wallet. Depends mostly on a decision to sell forked coins, as my private bitcoin key may become compromised (when going a sketchy s***coin wallet/exchange). But anyway, the question is about transferring from the paper wallet.