Include Page in layout?

I’ve got a set of links to the archive sections of my categories. They all work as usual. What I would like to do is in one of the category archives, instead of showing the posts it contain I would like to show a Page instead.

I know how to get it all working with the php i think but i’d like to know if and how I can can call my Page at a certain point?

I’ve got an If-loop to see if I’m on the right cat and when I am i’d like to call/include that page ID. Is that possible?