A noteworthy point mentioned above is that ANY solution, where at any time, the private keys/SEED words are online is a risk. You can help to mitigate that risk by encrypting your wallet, which will then encrypt the SEED. The better solution, again my opinion, is to use a hardware wallet so NO keys ever see online.
You can use an electrum wallet offline for cold storage, and transfer a transaction to a different online wallet to send coins. The cold storage wallet never needs to go online.
http://docs.electrum.org/en/latest/coldstorage.html
There is no SEED on a watching only wallet so you can't rebuild the wallet using SEED on that machine. To rebuild the online wallet (watching only computer) and its transactions, you would need to save the MPK (master public keys) from the cold storage wallet. Using the paradigm you describe you would never allow SEED on a watching only machine. As long as you have saved the SEED on the other machine you could always create a new wallet on the cold machine, and then copy/paste the MPKs to the watching only machine and rebuild that way. Therefore the offline/cold machine wouldn't contain any transactions or history since its never online. The watching only wallet contains all the history, and remember the same BTC addresses are created by bringing the MPKs over from the cold machine. Electrum makes this so easy!
The whole point of this is by saving ONE SEED LIST, it allows for complete recovery of both cold and hot machines. Its just for the hot you grab the MPKs from the cold to make it happen.