Trees, Shrubs and Conifers: Calling all tree experts! "Forcing" a new branch, 1 by dovey

dovey wrote:
My weeping cherry does all it's "weeping" on one side of the tree.
I assume the graft was lopsided.
(It was the only tree left, it's very healthy and I wanted it bad - lopsided or not)

I'm told that if you make a cut into the trunk, the cut will cause the tree to grow a new branch from the wound.
It seems like a simple solution and I'm ready to give it a shot.
My questions are:
Is it ok to do it now or what time of year it should be done?
How deep should I make the cut?
Thanks
Dove