Research shows that most of the troops involved at Stony Point would have been in French-made “contract coats” (aka “Lottery Coats”), supplemented by linen hunting shirts. Wayne comments to Washington in September 1779 that the clothing of the Light Infantry was “very Ragged–especially the Virginia Line whose coats are so worn out that they are Obliged to Substitute Linen hunting Shirts”. These hunting shirts were probably natural or off-white.
The Corps of Light Infantry had a difficult time becoming uniform, as Washington was not willing to apply too many resources to a temporary Corps. For that reason, some of the Corps had caps (either leather or felt “cap-hats”) and some had simple cocked hats. Wayne’s orders the day before state: “Every Officer & Soldier is then to fix a peice [sic] of white paper in the most Conspi[c]ous part of his Hat or Cap to Distinguish him from the Enemy”. Based on this information, either caps or hats are appropriate, with slips of white paper added to them.
Just after Stony Point, it can be documented that the battalion companies of the Virginia Line bought Nivernois style hats (4″ in the front, 3″ on the side, 5″ in the rear). The first mention specific mention of caps for the Virginian light companies comes in October 1779, “Gen’l Wayne has observed with Great Concern That the Virginians are the only troops in the Light Infantry that has not procured Hair for their Caps.”