How do I hard code the Recent Global Posts Widget into EVERY blog

I'd like to enable the Recent Global Posts Widget in the footer (or sidebar) of EVERY site (we use the same base theme) within our network of 20+ sites. Any easy way to do this? The display settings would be the same for all blogs, EXCEPT we would want to exclude posts from the blog the user is actually visiting.

For example:
- You are browsing blog 4
- We want to show the most recent posts from all blogs except 4

Is there a way to hard code it in?