Ta da! Instant success with this amazingly engineered prototype (patent pending)! A bit of soft wire from the garden, a length of wood I found in the cloakroom, and a small polythene sandwich bag, all reinforced with sellotape. I gave Poppy extra water in her lunch and waited till she needed to go out, having put the lead and everything ready, and it was all sorted in five minutes.
The two ends of the wire loop are wrapped around the stick, and taped. Bag edges go over the loop, pulled tight, and clipped or taped at the stick so the weight of the pee doesn't pull it off. Because the loop is oval it slipped easily between her legs, and the wire made it easy to adjust the angle - Poppy was completely unaware of it. If necessary you could snip a corner of the bag to fill the specimen bottle, but fortunately I had a suitable pipette!