Barbara, please don't choose angora. While it is soft and lovely, I saw a horrifying video a couple of weeks ago showing how in China (and hopefully NOT in this country) they just yank the hair out of the rabbits and they just scream in pain. Then, they are put back into their cages and fed until they regrow the hair, only to have it ripped out again. How cruel!

Wool is a good choice. Not a trim, but you can "thrum" the hat. I've never done it myself, but it looks easy enough. You should be able to find information and videos online for that process, too. It's often done for mittens, but you could use it around the brim of the hat or line the entire hat that way.

There arfe wonderful fuzzy synthetic yarns that would make a cute border to your hats. Yarns such as Boa and Fun fur would make a nice trim....and no rabbit guilt.
Or you could also crochet flowers and leaves to sew around the edge of the hats.

The Plymouth Yarn Company has an angora yarn that is made in Italy. There are 49 yards per ball. You can buy it in local yarn shops that carry good quality yarns. You can order it online from Jimmy Beans Wool. ($8 per ball.) JBW only charges $4 shipping, no matter how much you buy, but if you buy at least $75 worth of stuff the shipping is free. And, you earn 5% credit towards future purchases.

Webs is another yarn (and knitting/crocheting supplies) website that offers Plymouth angora yarn. One penny less expensive per ball than Jimmy Beans Wool. They charge shipping according to the package weight, but you can see their shipping charge chart by scrolling down the page on that link. They offer a discount on many of the yarns they carry (look for a little "price tag" symbol), and the Plymouth angora is one that does get the discount. If you buy $60 or more of discount-designated yarns (it doesn't have to be $60 of all the same yarn), you get 20% off, and it's 25% off $120 or more.

Plymouth does not have the angora yarn in an apricot color, but they have white, cream, and fawn, all of which might work for you. They do have two shades of pink -- "pink" and "medium pink." Right now, as I type this, JBW is out of the white, cream, and fawn colors, and they have 5 balls of the pink. You can place an order and if they are out of a color, they will fill your order when they get more in stock. You can call them to inquire when they expect to receive more. Webs currently is out of the white, but they have 31 balls of cream, 11 balls of pink, and 9 balls of fawn in stock.