My memory of solid axles is of either hex nuts or wing nuts for the front wheel (because you couldn't get enough tension on the back wheel with a wing nut to stop the wheel from slipping in horizontal dropouts). I don't remember any ever having a folding handle. Which isn't to say they didn't exist, but I never saw or had one.
I did have some that were asymmetric, so not exactly butterfly nuts. They looked a bit like an old fashioned oil can, with one long arm (like the oil can spout) and one short one (like the oil can trigger pump). You put your thumb against the short side and wrapped your fingers round the long side. Like this: