First off, Welcome to the Lounge, kwmpa!
I'm going to guess that you want Yacht Club, not U.S. Navy.
This has been a topic previously, but before Lancaster Caps went out of business. I got curious and did a few Google searches and came up with a yacht club uniform supply web site, Captain's Quarters. The cap they sell isn't a dead ringer (different chin strap) but very close. They only show the white one, but do have it in black. They do not state the material, but I'm sure they'll tell you if you ask.
You can then purchase the device to sew on the front:
Judging by the description the one the Skipper wore must have been the lowest rank in the club! (Member, according to the check-out choices.)
I hope this helps, and again, "Welcome aboard!"
Cheers,
Tom