If both of your computers can connect to the Internet, you don't really have a cold storage option. One computer should never be able to go online. You use use that offline machine to sign your transactions. You create the transaction on your online machine and save it on a USB drive. Connect that USB drive to your offline machine, load up the transaction in your cold storage computer and sign it. Save the signed transaction to your USB drive, bring it over to the PC that can go online and broadcast it.

You need to make sure that your cold storage can't go online ever. Remove the network adapter, or if you don't want to do that, never connect it to the Internet or WIFI. Also make sure your cold storage is malware-free. It's a good idea to reinstall the OS on it to make sure it's clean.