Visor caps should never stored or displayed resting on their visors! This will stress the sewing holding the visor to the band and eventually cause it to pull away. Some people display their caps on Styrofoam or manikin heads, but I find this somewhat stark and “disturbing”. I prefer a more non-anthropomorphic display. For the adventuresome types, you can get a bunch of bowling balls, cut them in half and mount your caps on them! I’ve heard of this done for very small collections. However, you can achieve the same effect much easier by using large soup bowls turned over. I use 7 ½” agatized wood bowls for most of my displays. As long as the cap’s band is supported and the visor doesn’t rest on the shelf, it will do famously. For fancier displays, you can cover the bowl with colored cloth or paint it (finishing with a clear coat to ensure the paint doesn’t rub off on your cap) before placing your cap on it.
Or you could display them on stuffed animals – although this takes up a lot of space!
Please note: I do have a number of excess tan agatized bowls for sale (same as I use) – for $1.00 each (very good price!). The only thing is that you will have to pay the exact mailing cost and these are somewhat heavy. I can estimate for you if interested and get them weighed.