We have many lovely photos taken by strangers during our travels both in the USA and Europe.
My husband is a photographer and his suggestions include labeling your camera with your name and contact info, silver permanent marker works well. He labels his camera body and each lens and his pack. He often takes photos of others and picks passers-by to take our photo. He will frame the photo and focus, so the volunteer just needs to push a button as if it was a point and shoot. Also keep your request simple - use Photo? instead of a complex "Please take our picture?"
Many people volunteer to take our photo and never once did it get stolen. Often you are in a place where they could not get away - on the top of the Eiffel or Arch for example. Nice people are every where! We have an excellent shot of us on a ski slope in the Dolomites :-) taken by a stranger with whom we had no common language - just an inquisitive "Photo?" and a friendly smile.
Once a volunteer kept backing up, stepping into a gap in a thick crowd, and I started to get nervous but eventually she framed me with the top of the Arch de Triumph and returned my camera with a smile. A great day with a parade of veterans relighting the permanent light for the unknown soldier.
Enjoy the trip and talk to strangers :-)