RE: Triggering Webshipper Extension
Follow below steps:
As you said you can access those from Front End.
Just open one that page
press Ctrl+Alt F1, you will the Page No. on the right sand box
Copy that Page No.
Now search and open the Webservice Page
Click on New button
Select Type as Page, paste that copied No., check mark on Publish field, copy that OData field's URL
Here you go, use that URL as GET method as your API.