Sturmey-Archer made gearboxes for some of the Douglas o.h.v. factory racers circa 1930-32, but these are quite rare. Only a handful were made.
Folks that sprint DT/SW models use the Norton 'dolls-head' gearbox, but this does need extensive modifications to mount. A platform needs to be welded to the back surface of the gearcase to enable it to be bolted in Douglas frame, laid down of course. Doing this securely, without distorting the case is not easy. There are at least two styles (probably more) of the dolls-head box, excluding close ratio ones. There is a earlier version with bronze layshaft bearings, and then there is one with ball bearings. You need to be careful if getting a pile of bits that they all are for the same style 'box.
Most sprinters discard the Douglas flywheel clutch and use the transmission mounted Norton clutch.
-Doug