Rule of thumb says "if it bent cold without cracking it will straighten same way"
Many ways to try depending on equipment available. Best to apply force in controlled way by press/clamp etc but tube/lever is OK
Worth placing a piece of wood between barrel and lever at point of bend then squeeze them together with both hands or a clamp.
The barrel will stand it.
Don't understand cocking shoe ref. The 77 doesn't have one.