The lampholder contacts on the top of the adaptor look like brass screws.
They are. It was a common arrangement on these adapters. Some had a slightly different arrangement in which the contacts were a flat head (sometimes hex shaped) set into the recess, then the screws to secure them went in from the sleeves of the 5A socket.
I would imagine that any cord you used on the plug would have to be reasonably light
Maybe if the plug contacts closed up (or the sleeves in the socket opened out), but the old 5A plugs can be a surprisingly tight fit.
The "splayed out cotter pin" style prongs of the plug pictured always used to hold very firmly.