Connecting multiple data entities to the user object
You would probably be best to create a Shipping Address content type. You should also look at the Address Field module to collect the addresses rather than field collection.

Then you can create a simple view to list the shipping addresses (Node Tile not linked) using a contextual filter on uid. Then set up a node reference field in your webform using the view to provide the values. The user can then select which shipping address to use for his order.

On the user page you mav use the same view (separate display listing titles as edit links) to let them edit their shipping addresses, and give them a link to add new addresses if necessary.