First of all, nofollowing your links will not prevent you from losing link juice. In general, you do not ever want to nofollow your own pages.
If you really want to prevent link juice from going to your Contact page, you could use Javascript instead of an HTML link. However, this will break if the user does not have Javascript enabled.
In the big scheme of things, it is probably not worth your time worrying about linking to your Contact page. Link juice that goes to your Contact page is not lost, since the Contact page itself also links to your homepages and other pages, and thus keeps the link equity flowing.
As far as site architecture goes, just link prominently to your most important pages and less prominently to your secondary ones. Then focus your efforts on acquiring more links, because that will have more impact than fiddling with some links on your page.