I don't think that the Express versions of Visual Studio support AddIns. However, the only reason you need the SF AddIn is to launch the BOMapper. So, you could have your business objects in a project that you open and manage with Visual Studio and then just reference that project in the Web Developer edition. All of the type editors should work fine.
There is also the option of downloading the Web Developer that runs inside of Visual Studio. I believe it's called the Microsoft Web Developer Tools. I haven't looked at Web Developer Express, but I would assume that they are similar.