Promises are a client side concern exclusively. You do not need to do anything from Wakanda Server other than return a result (as you already have been doing) using the httpRequestHandler. How you handle the request client side is your choice.
The fact that your server side code is making a request to a third party does not affect how you would approach the browser's async nature (be it promises or callbacks). Your Wakanda Server code will be synchronous and wait for a response. In turn, when the server side request is complete, including the request to the 3rd party, it will respond to your browser.
With Wakanda Server being multi-threaded, synchronous code for the request will not block other requests from being fulfilled.
I hope this helps.