Apart from an "o" for an open hat and an "x" note for a rim click, I don't think there's any other kit-specific notation. Like most instruments, a technique is usually written out or abbreviated, such as pizz. (for pizzicato.)
I suppose you could just write "edge" in the appropriate sections, or for one note at a time where writing space is limited, use a unique symbol - an asterisk perhaps? - and note at the top of the piece that an asterisk equals the hh edge.
Necessity is... etc etc.
PS - I made a correction, a trill does have a physical symbol, a jagged line.
I guess it would depend on how many other things you're trying to notate. If room on the staff is available, and it's constant enough to need it, give it its own line. If not, as Bermuda said, the drummer should be able to gather that they need to edge the hats.