Does the World Swapper modifies the F18.exe while switching theater? I'm wondering, because I don't understand why the compatibility option applied on the F18.exe has influence on the fact that the right missions will show up in Single Mission menu?
This problem I have seen before. The reason you can't see the missions, is because the folder holding the missions doesn't have the right permissions for the game (f18.exe) to see them. I'm pretty sure that changing compatibility mode on a .exe file changes the permissions. The World swapper does make changes to the registry pointing the f18.exe to a different mission folder depending on what world you select.
From the TSHv2 readme "Once a theatre is selected in the swapper, the following registry entries are modified to point to either the Iraq folder or the Ncape folder". Try giving the worldswapper.exe and TSHv3manager.exe the same compatibility mode that you have set on f18.exe. You might check the Mission folder and Iraqmission folder permissions as well.
I don't know what version of windows you have issues on, you mention XP and win7-both handle permissions differently. Installing the
F/A-18 Full Install to TSHv3.06 to the root of C:\ will probably make all the permissions equal on the folders and files.