You can offline sign with Core if you're willing to go the extra step.
Don't delete the old wallet. Always keep a copy of your old wallets, you could need these keys in 10/20/30 years.
...
Make a paper wallet backup of Armory private keys.
Semi right steps, wrong order. This is the proper way to go about it:
2) Create backup of said wallet.
3) Test the backup.
4) Test the backup again
5) Once more for the good measure
6.a) Create WO wallet and export it to your online machine, then sync it with the network. Grab the address from your WO wallet. This prevents address reuse if you intent to give the wallet some traffic, while letting you keep an eye on your funds.
or
6.b) If this is a long term cold storage wallet and you don't intent to sync it for a while, grab the receive address straight from the offline wallet.
7) Did I mention testing your backup?