Many thanks for the suggestions - I should have mentioned it would be primarily for old arcade games (Galaga, Joust etc). I use a PS4 Bluetooth joystick for other stuff.
The HORI Mini looks interesting, but at under 4" square (if the Amazon details are to be believed) it's perhaps a bit too small.
Sadly, making anything myself is out of the question - I am probably the single most inept person on the planet where that sort of stuff is concerned. Last time I tried soldering something I ended up welding the cat to a table, and we don't even have a cat..!
However, my Google-fu seems to be improving so I'll go take another look and see what takes my fancy.
Many thanks, all.