You wouldn't use Dwolla payment buttons for scenario. You can simply integrate with our Off-Site Gateway API. Check out the Server-to-Server workflow here.
Essentially, your webapp will POST to Dwolla some details about the checkout you’re trying to create (destination, amount, etc.) and Dwolla will respond with a CheckoutId.
From there, you'll use the CheckoutId to construct a URL which you'll send the user off to by means of a redirect or a link.
Here's a demo of what this flow would look like to a user.