Add small buttons inside tree

[noamway]

Hi,

I have a tree with a list of pages and I like to add a button to the right of every page in the tree.
This icon will use me to open a the user a drop menu that I already open with the right click method.

Today most of my user don't know they can "right click" every page in the menu so I really like to give them the option to see this button.

I attache an example where I need the button and I really like to know what is the best way to do that.

Thanks,
Noam