The white uniform was for summer wear, the grey for winter. The "funny looking" flat hats were and are worn by most of the worlds navies. My company in boot camp was the last issued the US Navy flat hat, although the only place it was worn was in the Med. The white cuffs and collars were standard for both navies, piping was initially a personal adornment, but was made official about 1863 by the Union Navy. Enjoy naval re-enacting and I'll see on deck some where, welcome aboard.
John R Denley
POIC
Memphis Detachment
CS Navy