Are you needing to get existing supporting documents/attachments from PLM for Process to your site, or the other way around?
Is the Part Number stored as a cross reference on the specification, or is it the name of the supporting document? What type of Specification(s) would you be retrieving the data from?
You could probably write a custom web service that takes in your PN and returns the attachment. We have a reference web service along with documentation in the Extensibility Pack, in the ReferenceImplementations\ReferenceWebServices folder. Of course, the logic in the web service would be different, but this example and documentation helps guide you in creating a web service.