You can play Twilight Princess without needing knowledge of Ocarina of Time. The sages make it pretty clear why Ganondorf is being executed. Now if you play OoT you understand that Link sort of tipped the royal family off that Ganondorf is evil. I don't think one needs to know that to play TP...
Aw my stomach. It's ok I'll just let all my gastric acid pour out internally. Somehow I'll live another... let's say 20 years? Maybe my magic can heal me?