You can assign shortcut keys to actions by using the Action Options from the actions panel flyout menu.
You can also record a batch action if you want to run something on your open files.
I don't believe there is an easy low risk way in newer versions of photoshop to add menu items to the menu that pops up when right clicking on an image.
(versions after photoshop 3)
Thank you very much for the reply. I apologize for the very very late response. Did not get an email saying there was an answer..