If you don't want a style to be available from the menu then edit your stylesheet and add all the styles that you want removed from the style listing.
For example if you don't want the Text style to appear then add this cell to your stylesheet:
Cell[StyleData["Text"],
StyleMenuListing->None]
Do this for all styles that you want to remove from the style listing.
Cell[StyleData["Style#1ThatIWantRemoved"],
StyleMenuListing->None]
Cell[StyleData["Style#2ThatIWantRemoved"],
StyleMenuListing->None]
etc.
Or alternatively just add empty cells for each of your unwanted styles (you can do this from "Choose A Style" pull down menu in the Edit Stylesheet notebook) and then select all of those styles you just added and make the change via the Options Inspector
