I'm not sure if there is an API call for it, but you could go to Audience->device tokens, and make a script to fetch all of them.
In the company I work, we decided on a different approach.
All communication with Urban Airships goes through our own backend, where we at the same time store the devicetokens sent from the device. That way we can shift to another way of sending push notifications without modifying our apps. It is of course a bit more time consuming to do the initial development. On the other hand, if you go for the solution you are currently considering, the switch to you own implementation (or another push provider) will properly require several migrations, or at least maintaining two different ways of sending push notification for a considerable time.
BTW:we have been using UA for almost 3 years, and have been very happy with their service.