OK, found a way to remove the headers and footers without deleting the _sub_header and _sub_footer includes. In case anyone else is looking for it, here's the quick and nasty - I'll probably play some more but this is it so far.
Obviously first step, in admin builders set the chat menu item to open in a new window.
Then in templates/base copied _sub_header.html to new file _sub_headerchat.html and copied_sub_footer.html to new file _sub_footerchat.html. If you're not using the uni template, you probably need to do this in your template folder.
Then edited the new subheader and subfooter files and removed what I don't want - e.g. from footer I deleted _bottom_links_ and _copyright_, from header I deleted __top_menu__ and __top_menu_breadcrumb__.
Finally in /modules/boonex/chat/templates/base/page_57.html renamed _sub_header to _sub_headerchat and renamed _sub_footer to _sub_footerchat.
Now someone will tell me there's a much easier way :)