Purple Medallions Handkerchief (pictured left): purple is THE color of the season. This handkerchief would go great with a dark suit and a white collared shirt. It's always nice to add a little color to your outfit. 100% cotton. The handkerchief is $9.
Silver Crown Tie Pin (pictured right): a tie pin -- as distinct from a tie bar -- is great for knit ties, which are usually made from cotton and thus a vegan man's friend. I think a tie pin is a great way to dress up what might be considered a less-formal tie. I particularly like the subtle yet regal crown design of this pin. Made from silver, it's $15. Tangentially, Fine and Dandy sells tie bars and cuff links that are engravable, which I find interesting, but ultimately think would be pretentious.
I also really like these Navy Diamond Marcoliani Socks (66% some type of vegan fiber, 33% nylon; $15). There's nothing like a good pair of socks with a touch of diamonds.