I'm not sure about the portion along the Highline trail below the rim, but above the rim, there's some low marshy spots with leftover snowmelt in spring, but in general I would not count on finding any water. But a hike down toward Woods Canyon Lake will solve your problem. Of course, if the campground is open, there's a store and potable water anyway, but that sort of ruins the fun, huh?
You might want to read some of the triplogs for the Highline Trail. I would think that the Sharp Creek drainage would be your best bet, but even so, with no recent precipitation, I wouldn't count on it. Hopefully somebody who has hiked that portion will be able to confirm/deny for you.