I was curious and got online...found out that some caps are available in the Women's Wear accessory areas of department stores. Really!

Today, I went to Target, J.C. Penny, and Ross. Target has a black cap with elastic in back and a short bill: "Newsboy Hat Black/95291 @$9.99. It has a mix of materials, not pure cotton or wool. Ross had a 100% cotton black cap, short bill, similar to those quilted welder's caps (see Francis Whitaker): D&Y Brand @$5.99. J.C. Penny did not have a very good selection in my city, but they do show a few on line. These caps are sometimes called "newsboy" and sometimes called "mod caps."

This kind of cap was worn by some workers, for example, the Dutch boy pictured in the trademark for Dutch Boy Paints. In recents years, the cap has been coopted by the Women's fashion designers.

Some of the mail order sites say "Fits Most," but I wouldn't buy a pig in a poke. I'd want to try it on in person.

http://www.turleyforge.com Granddaddy of Blacksmith Schools

check out the australian baggy green cricket cap or the old style english style cricket caps

I've been a Boilermaker/blacksmith for 25 yrs and have tried every cap the stores had to offer. Long billed ones, short ones. I bought five off a man at work who's wife made at home. I wore them everyday. Still got three of them.
Point being. She explained why they last so long and so comfortable. She placed the seam on the inside slightly of center. Instead of center of you nose, more towards your ear. This was to keep your welding hood,face mask head band for digging into your forehead after all day.
And she washed the material many times before building the caps. To be soft. Store bought ones are rough and shrink to much.
I suggest. Getting someone that can sow and take a store bought one and de-construct it for a pattern. But move that seam over some. That way you can find the color, or pattern you wish to be period correct.
This man could sale grocery sacks full on the job every other day. His wife worked on site but quit cause she made more make hats. Funny fabric designs too. Hawaii looking ones, camouflage, ball teams. That material was from Walmart just two plyied around headband and on bill. Which worn backwards deflects fireballs off you neck And if laying down welding, turn bill around To cover ears. Or hair, ponytails. Whatever. Helps keep sweat out your eyes. Most all welding supply offer komex caps or tractor supply stores too.
Sorry such a long post but never worked a day without wearing one all.day long. It'll save your hair from falling out too, if you wear a hatdhat. Maybe. Not guaranteing that one. But I still got mine. If anyone has trouble finding some let me know. I Got drawers full that are to.little. after washing.