How about the new Samsung Galaxy Xcover 2 with these features:
- dust proof
- water proof
- 4 inch screen
- camera button (easy to press, even with gloves) with power LED flash
- strap holder so difficult to drop
- fast Android operating system.
There is a very fair review of the smartphone here http://www.phonearena.com/reviews/Samsung-Galaxy-Xcover-2-Review_id3244. You can buy from all of the usual Internet phone shops for under £200.