the old Sturmey archer hubs are a bit less than that wide. Same with old Shimano 3 speeds
could fit washers to make up the gap
The shifters often have the cable with full length outer casing. So you just zip tie it to the frame.
But the cable clamp to go on the rear stays maybe tricky. They do come in some different sizes. but all about the diameter of a little finger.
Also the shifters will be for 22mm bars.