If that would be as easy - there would be tons of flash applications with facebook like icon.
Overlays are much much much easier and it is a natural way to add LIKE button. Facebook Like button workaraunds would work until facebook would change communication protocol. If facebook would change something - all your tours which rely on flash workarounds would break, but overlays would survive, because the html(overlay) button is being created by facebook itself.
Imho, it is in your interests to use overlays ;-)
My Tourweaver components: http://www.optitecha.lt/categories/3