Just about any GSTP watch of that era will do. There was no "standard issue" watch for the 19 set. None of the kit lists show a watch as an issued item. The WS11 kit had one listed as "watches, non-magnetic, WT" and the WS52 had one but it was deleted from the kit list. There was a VAOS number for the watch (VC7563) so I suspect there were many makers whose order went into the pot and when you needed one you took "pot luck".
As to the stem issue I've seen photos of both ring and ringless watches used. In fact the original manual for the WS11 shows a photo of a watch with a ring.
There is a good article on British issue watches here:
http://www.kilocycles.co.uk/photos/watch.htm