Let's say I'm running IG88-C and IG88-D Crew on a ship with no evade action. Can that ship still take the evade action as part of the IG88-D/C crew interaction? Or does the ship need access to an evade (built in or otherwise) in order to take the evade action as part of the ability?

You can take the free evade action, you don’t need evade on your action bar.