Hi Dave, you do not need to use a stringline at all. You just place your foundation stones in place so that the walling edge of the faces follows the curves you desire. Once the footings are in for the whole length of the wall, working uphill, all you need to do is to build each course of the wall using your EYES to make sure each course follows the curves of the footings.
I wouldn't advise putting lots of stakes in to give you your line. Your hosepipe idea should work fine enough.
Erect the wall in short (1 to 2 metres at a time) keeping all your courses running horizontally, and make sure that the stones go lengthwise into the wall and not sideways on. Also beware of using long front faced stones on any of the curved bits, they can easily send you off line giving flat bits on curves ( as can the use of stringlines).
If you just use your eyes and are honest with yourself (ie if it doesn't look right it probably isn't. I wouldn't worry about batter frames as they are useless on curves. It is nearly impossible to build a vertical faced wall, your danger would be putting too much batter on. You can decide the batter you need and can buy a long bubble level, set it to the batter you need and use it.
A couple of photos of the site would help.
I too live and work in a mountainous region of England, The Lake District, and I can't remember the last wall we built that was on flat land with no curves. I just love building curved walls going up steep hillsides.
Have a happy positive walling time.