The "snapping" tool seems to only be attached to the editor tool and I want to be able to label some important points on my shapefile.
I think that you have a graphic draw and you want to snap feature in edit session. Isn't That?
as the following picture, you can convert your graphic to features and you can snap easily.
The snapping tool only works for geographic data not graphic data generated from the Draw Toolbar. As mentioned above, you can convert graphics to features and then snap.