How can I do this without importing my current private key into to a "live" computer connected to
the internet? That is to say, even if I build a new Linux computer, install core, import the key,
create a transaction (internet disconnected)... connect to the internet to allow it to broadcast - if
my opsec is broken somewhere - some rogue software could still create an alternative transaction
and broadcast that instead.
Use Electrum, make two wallets, one normal wallet on the offline machine, other "Watch Only" on the online one, make the transaction on the online one, transfer it to the offline one, sign it, bring it back, broadcast it.
Tutorials here:
http://docs.electrum.org/en/latest/coldstorage.html#cold-storagehttp://docs.electrum.org/en/latest/coldstorage.html#create-a-watching-only-version-of-your-walletFor more security, use an address for one transaction only, send the rest of the balance into the next cold storage address.