I took a second look at your request. As for photos, most units did not have their group photo taken. Also, a photo was not taken by the government as part of the recruiting process. Photos that have survived are almost all ones paid for by the individual soldier ( big expense, as Yankee privates were paid $14 per month, and many artists charged 3 bucks or more). If a hat shows in a photo, it was a selection by the individual.
As for regulations, I searched the 300 + books in my WBTS Library, and came up with a few requirements for headgear. The best being "Don Troiani's Civil War, Cavalry & Artillery". Don is well known for his very accurate portrayal of uniforms, and he list several regulations. The second work is "United States Army Headgear, 1855-1902". Don't let the title throw you, as the Hardee used by several services was an outgrowth of previous cavalry patterns.
If you would like me to copy the info, send me your email address, and I'll reply asking for your mailing address. Bill