Delta uses gates at Terminal B, at least in my experience. Yes, if you have checked bags, you will have to retrieve them off of the conveyor belt and then go back through security to get to Cape Air, which uses Terminal D (and it's a trek, let me tell you).

If you have Global Entry, you can hopefully avoid a long wait in the security line; under the best of circumstances you might get through in half an hour, but this is an extremely difficult thing to estimate so be prepared for it to take as long as an hour.

Going through that airport is always the worst part of my trip to VG. A tip about taking bags onto Cape Air - if you have checked bags from your departure airport that have stuff in them which might violate TASA carry-on regulations, you can check them at the Cape Air desk that is in the main terminal (i.e., before you pass through security), and while you can thereby avoid having to schlep it down to Terminal D, you'll get charged a fee for it.