Hmm, I think you'd have to delve into code for that.

Are you able to allocate such posts to their own category?

If so, you can use a plugin like 'Category Visibility' (not tried it personally) to exclude that category of posts. Does that work for this case?

Here is a custom recent posts widget that allows you to specify which categories are to be included or excluded from the list of recent posts.

Wordpress Plugins - Red Blue Recent Posts Plugin

Was this what you were looking for?

Sarah,

Have you tried my plugin?

I've now added a checkbox to every post so that you can exclude single posts from recent posts widget as well.

Red Blue Websites Wordpress Plugin | Red Blue Websites