You are correct that you should not put your database file on a shared drive or file server. Databases are fundamentally different from the normal, document-based files that would typically go on such drives; that route would be a sure path to database corruption.
Is there a reason that you're not considering using FileMaker Server, which is the safest, most robust way to host a database file for multiple-user access? If you cannot set up a local machine to run FileMaker Server, you might consider using a hosting service. (Search the forum for hosting service; you'll find multiple hits.)
A FileMaker database should only be share by FileMaker Pro or FileMaker server. FileMaker Pro can open a file sitting on a network share however this can be a recipe for disaster. With nothing to protect it, any number of issues can cause the copy of FileMaker Pro to disconnect from an open database. If this happens it may cause the database to become corrupted. So when you have a copy of FIleMaker Pro host a file, the file should be on the local disk drive.
I believe that Go can only connect to a local file on the iPad or iPhone, a file shared by FIleMaker Pro or a file share by FileMaker Server.
So I think this leads you back to a discussion with your IT department. Either they let one computer act as a FIleMaker host for the file or setup a FileMaker server for the company.
You can include in this that you are not adding a file share on your computer, you are having FIleMaker Pro provide a hosting service, and only FileMaker Pro and FileMaker Go clients will be able to access it. So a much smaller security issue.
Good question. FileMaker is designed for this kind of sharing. As you know one of your options is peer to peer, or client, sharing. That will allow you to share with up to 4 other workstations, YAY! In your situation, it sounds like you can benefit from this; however, you have to share from a workstation on your network--like a server. If your IT department says "no"...
You are left with the second, and best option, FileMaker Server. You can read lots about that here.
You may explain to your IT department that the other users would only be able to access the file, not everything on your computer.
Talk to the IT department. Filemaker will only allow connection through one port and only that file can be accessed. If setup properly only specified computers on the company network can have access.
Running peer to peer uses some resources on the hosting computer and the regular processes slow the sharing performance compared to a dedicated server. I used Peer to Peer with only 7 users (R12 allowed up to 9 clients) for a while before switching to FM Server. I was not happy with the cost as we needed a Server to stay current and support the existing clients we had on Peer to Peer. Amazing difference if you can justify the cost and your IT department might like the idea of a small server better. Give them something to look after.