Hi Steve,
I believe this is the CLSID you are looking for.
{BD43551C-5313-11D2-87B8-0000F8751720}
Here is how you find it.
In ArcMap go to Customize > Customize Mode
When the Customize window opens on the Toolbars tab place a check in the Context Menus box.
A Context Menu opens, click on the drop down icon
Here's the fun part - find the context menu you are looking for matching it up exactly. In this case "Element Context Menu". Once you have that name open RegEdit and search for the name you just found.
I know you are looking for the "Properties" menu, that should be a subtype off of the CLSID you find.
TIP: Capture a screen shot of the Context Menu you are looking for so you can make sure you have the correct menu.
Good Luck,
NOTE: If you don't find the context menu you are looking for in the list of Context Menus then it means that the context menu is not customizable.
G