I don´t think that you will be able to disable the New menu and in any case,
you would have to do it only when the IDE has your solution loaded, not
always! There are solutions add-ins, that is, add-ins that are
solution-specific and not general. Maybe you can create one of them that
disables or intercepts the File.AddNewProject command.

But in general, if users are outside your company, they should be able to do
whatever they want with their solutions. If they are in your company and all
this is only for a specific company project, you can use SourceSafe and
checkout exclusively the solution file.

Just a few pointers...