Can I list categories for a post but always exclude a category

When displaying a single post, I want to create a series of links at the top which display the categories in a horizontal list with “>” between them. (to appear like cookie crumbs).

I have figured out how to do this using “the_categories” and changing the seperator to “>”. However, I can’t figure out how to exclude certain categories from displaying. I know that you can exclude certain categories from “wp_list_cats”, but can you do it with “the_categories” tag? Does anyone have a work around?

I want to exclude a certain category from displaying because I use that category to place certain posts in a feed which displays those posts as headlines on all pages. However, I don’t necessarily want that “headline” category displayed in the list of categories for the post.