There isn’t an easy way to do what you ask, actually I don’t know of any. Once SW starts and loads the add-in DLL’s, you can’t do anything to them until SW is closed. In the past, I would create a separate thread in my DLL to check for updates on start or exit and just notify the user to update when SW is closed.
The only way that works for us is to load it into EPDM since it essentially keeps an up to date local copy of the network file on each user's PC. This only works if you have EPDM though.
Create an installer using Visual Studio, Wix Toolset, Install Anywhere, Install Shield, etc...
What if they have SolidWorks open when the update occurs? Is the registry going to like your network location?
There are ways of getting your addin to update automatically by looking at the network drive for the newest version but these all require some kind of helper program or script and this is probably beyond what you want.
What I would recommend is that your addin simply look at your network drive to determine what the latest version is and whether this corresponds to the current local version. (For example, it could look at the name of the MSI, which could contain the addin version.) If they differ then the user is told to close SolidWorks, get the latest MSI, reinstall, and open SolidWorks.