Consider a generation not used to the analogue wrist-watch, and give them a clock face with an outer 24-hour clock and an inner 12 hour clock, and then ask the user to select time using the tip of their finger, on a small phone screen, on the inner or outer circle to the hour and minute that they wish.
http://3.bp.blogspot.com/-SK2ljlhHiCU/UaiEjF1lhGI/AAAAAAABJq...
Oh, and that top bit... the time that most people would read and want to change? Yeah, that's just display. Tapping that does nothing useful, just flips the mode from hours to minutes but you can't change the time that way.
So: A modal interface, on a circular control, with small areas of touch, that you cannot navigate one-handed accurately, and that uses the least popular display of time.