I want to use segwit! Do I need to create a new wallet?
I am running my offline machine armory wallet in this way "armory --force-enable-segwit --offline"
No, your current Armory wallet supports them, and you have the correct flags passed into the offline machine
You will, however, have to create new segwit addresses. In Armory these are P2SH-P2WPKH addresses.
File > Settings > Fee & Address Types
Alter "Preferred Receive Address Type" to P2SH-P2WPKH and any newly generated receive addresses will be segwit addresses by default. You can do this for "Change Address Type" too if you desire.
How I sign a segwit transaction on my offline machine?
The same as a normal/legacy transaction, but it of course must involve P2SH-P2WPKH input addresses.