Firstly if I'm in the fringe I don't expect to hole the putt / pitch. Manage your expectations go for par.
Secondly, if it's regular fringe i.e. a foot or so around the edge of a green I add a foot ( 1ft ) to my normal calculation, 90% of the time that gets me within 3ft for an easy par.
I prefer putting than pitch / chipping as I find it easier to read the green rather than judge where the ball is going to land and at what speed to judge the slope from a pitch / chip. Of course if there is a bunker or other obstruction or a very seriously sloping part of the green then I'll go for a different shot. For the stats freaks this is not good as it will adversely effect your putting average as it is rare (but not unheard of) to hole from the fringe.