Charle,
I had the same problem. You can change the signature by editing it on each email you compose, but the default is a bit hidden.
If you go to the the unified inbox at the top left is an envelope, touch that and select account settings, scroll down and under sending mail section you can edit or turn off the signature.
I had to contact Planet Computers to sort this. Not aware of a user guide for Airmail but that would have helped.
Steve.