Alican, as you might have noticed FB connect button doesn't have a direct URL. Functionality of this button is connected to Oxwall's core code and to FB connect plugin. That is why you will not be able to insert this button easily into the Custom Html widget OR into external custom page.
What I suggest doing is adding an image into your custom html widget or external page using simple .html code: <a href="
urloflink"><img src="
urlofimage" alt="
some_text">
</a>
where
urloflink will be a sign in page (
www.sitename.com/sign-in). Once users click on your button, they will be redirected to sign in page, where they will need to click on our standard FB connect button and log in.