Not sure the question was answered. Since the question was about "small ships" I assume "river ships" was not in question. I could be wrong, but I did not look up river ships. I went to "Small Ships & River Cruises" and selected near the bottom left column in blue: Grand Circle Cruise Line, then selected Small Ships.
Not sure what part of the world you are interested in or if your question is generic for any location/ship. I looked at each category of ship:
Mediterranean: Small Ships. 2 single rooms next to crew's quarters w/fixed port hole, less square footage; amenities except balcony is the same as "upstairs" rooms
Panama: MS Discovery. mentions "four twin bed rooms" does not mention anything about single rooms. I saw this very small ship while on a different company's tour and cruising the canal on a ferry type ship, last week. Discovery is really very small, much, much smaller than the Mediterranean small ships (Athena, Arethusa"). Don't know how they get that many rooms on the Discovery. People were swimming in the canal near their ship and snorkeling.
Antarctic: does not mention "single" rooms
Burma: mentions "8 twin deluxe rooms, 6 twin w/balcony rooms, 2 premier w/double beds and 2 single rooms" I think the best is to select the trip you want and look at the deck plan in the catalog or on line for that ship, then talk to Grand Circle. As for the supplement, I did not look any up because this depends on what GCT has advertised or has maintained as policy and these can change. Also, I wondered what "twin deluxe" meant: does it mean two twin beds without balcony, or one twin bed in those cabins. I think it meant two twin beds no balcony, and the other two twin beds with balcony. But, I'm not sure of that, either. As for getting upgraded from single to "upstairs". I've been on ships where singles are on the same level as the "couple" rooms. Is that an upgrade, or only rooms available and don't want to sail with empty rooms and lose $$? We've never been upgraded--always have to pay the supplement to have a balcony room or "better" room, according to the category and location on the ship we want.