The answer to both questions is, not if you don’t want to. If the idea of wearing a garter doesn’t bother you but the toss does than wear one and skip the toss.
Some brides will wear a garter with a blue detail for their something blue or a family heirloom as their something old.
If you want to keep the tradition you’ll easily find garters online in both frilly and fashion-forward designs. (I recommend designer/shop Garter Girl by Julianne Smith) There are garters in every color as well as every color combination and you can find themed garters too. I recently saw garters in college colors with mascot charms (not at Garter Girl).
If your fiance wants to do the toss you should tell him to keep it G or PG-rated because of your comfort level.