While Rhinoplasty can be performed without dedicated bone work, it is not the most common situation that I encounter. This so called 'finess rhinoplasty' is just a surgery where a patient has little to no profile hump and tip work is all that is required. Other physicians call this a tip-plasty.
Width issues with the nose can be due to skin, bone, or cartilage problems. In the tip, it is usually large cartilages, which can be reduced in size and remodeled with sutures.
If your nose is crooked, as you suggest, then the likelihood of correction without doing bone work is also limited. There are patients with deviated noses that do not require it, but that is a selected minority. There is no way to straighten bone without breaking it.
Your situation seem complicated enough that a formal consultation would likely help you to understand your goals and potential limitations. I would suggest that as the next step for you.