Found that I didn’t have any ‘one-size smaller’ M4 nuts, only some rather ill-proportioned commercial ones, so made some..
I didn’t have any 6mm hex. so ‘hexed’ enough 8mm round-stock to make 6 nuts plus cutting allowance in a collet block, transferred that to the lathe and drilled 3.3mm with a stub drill followed by a 4mm tap, ‘scored’ a witness with a 1.5 grooving tool before cutting off with junior hacksaw and facing-up the next- I didn’t feel inclined to part off 6mm stock with a 4mm hole in it at that distance from the collet.
I already had a small ali. billet with a 4mm thread that I’d used to face the studs to length, so locked a stud into the back of that to make a small arbor on which to face the sawn side of each nut before knocking the corners off each face with a file.