I'd personally go for the smallest possible classic warship designations applicable.
- If you want easily associable late 20th century, corvette is probably the way to go. Those are the warships the most closely matching small survey ships of today in size and design.
- If you want WWII, some sort of an escort might be your bet. The Flower
corvettes were essentially armed whalers, while the assorted sloops and frigates of the era were more like miniature destroyers, so again corvette might get my votes. But that's sort of British - destroyer escort would be the American option, although it sounds clumsy to me.
- You can go back to the sailing days, too - the Royal Navy certainly did when "inventing" names for its innovative WWII vessels. A Starfleet sloop or brig might sound funny, though, to modern ears.
- Perhaps the tiny vessel isn't really a ship (save in the sense a runabout can be called "starship" by a pompous pilot), though. "Patrol boat" would be quite fitting, too.