While a citizen's hat will be just fine for Picket Post, miscellaneous kepis are not going to fly.  If you would like an exact reproduction of the Richmond Clothing Bureau cap produced in 1863, however, Conor Timoney will be doing a run of them.  These will include a machine-bound oilcloth covered pasteboard visor, oilcloth chinstrap, oilcloth sweatband, and lining and visor welt indicative of these mid-war caps.  The particular original copied here is made from a dark grey wool on white cotton jeans, with a mismatched jeans visor welt, and oilcloth crown lining.
 
For more information on the caps produced in Richmond during the first half of the war, check out: 
https://www.libertyrifles.org/research/uniforms-equipment/richmond-cap