How to diagnose right-click menu slowness?

I believe that not there is an application that diagnoses what you want, what you can do is disable each menu item to find out what is causing the slowness.

Update

Looks like I was wrong, yes there is a program to diagnose the slowness, the program is Debug Diagnostics Tool

The DebugDiag tool is designed to assist in troubleshooting issues such as hangs, slow performance, memory leaks or memory fragmentation, and crashes in any user-mode process...

For exampleShellExView should work for you.

This utility works on any version of Windows, starting from Windows 98 and up to Windows 7. x64 versions of Windows are also supported.