Like Pat said.
If your tips and handle area all line up, no need to straighten. It might make things a bit more challenging. However the less material the easier it is to make heat corrections. If it was my piece and I wanted to make corrections I'd floor tiller like Pat suggested, taper to tips but leave an inch or so wide at tips, make my corrections, then narrow the tips to better line the string up to where i want(usually after tillering to a low brace height). TBH looks like there is more going on with that piece than I can tell from the pic, maybe some twist. A stiff handle bow with 55" of lenght will be difficult task if you plan on drawing past 23", for me anyway. But I understand, how you work with what you can get. been there, done that. Good luck, keep posting pics and questions.
Mike