Thanks for your post.
What you suggest is actually simpler than your questions suggest. What it will require before you get to the FileMaker part of things is to map the central network drive to each user's system in such a way that all users would be using the same windows file path to the file folder containing your files, for example 'N:/Data files'.
Once the mapping is done you would add a container field to your database to hold a link to the file in question. Add this to your layout and then go into browse mode. Click on the container field and navigate to your insert menu, or right click in the field and you will be given a menu with the insert options. Choose Insert File, and you will be given a browse file dialogue box. Make sure you are using the same file path to the file as your users would be and navigate to the file. Then at the bottom of the window will be a check box to store the file as a reference. This will save the file path as a hyperlink to that file path once you confirm the file selection.
The reason for setting up and using a unified file path in the way described above is because the file path saved in the hyperlink will only work locally to the user's system, so if the file is not in the designated file path location for one user while it is for another the first user will get prompted with an error that the file can't be found while the second can use it normally.
As prebuilt example of the container field usage is contained in the Document Library starter solution if you need a design to look at. there is also a script built into that solution attached to a button to give you an idea of how to design a more user-friendly interface to add files, images or other objects into a container.
Please keep me updated with any questions you have in this regard and I can go into better detail or clarify things as needed.