Ah, yes. I don’t have one of your adapters, but they sound like they might be perfect for a game like Thrust, which really needs at least one extra button, ideally. (At a pinch, though, Down could be mapped to thrust, if you didn’t have such an adapter. It would then be an “interesting” challenge to see if Thrust was actually playable with such a weird set of controls!)
The joystick adapter I currently use only has one input socket, for an Atari-style plug — and one output, which plugs into the Beeb’s analogue port. It only enables one fire button.