Would you recommend that I get rhinoplasty without insurance?

Your question brings up several issues.
One issue is whether a CT scan will be ordered. A CT is not necessary for evaluation of the external shape of the nose. That assessment is done by the surgeon looking at the nose and in the nose, and by feeling the nose. A CT scan would be required if there is suspicion of sinus disease or maxillofacial trauma.
A second issue is that of insurance. Improving the appearance of the nose is not covered by insurance anyway, so the point is moot. Plus, many (most) insurance policies do not cover complications arising from cosmetic surgery. Example: patient has an intra-operative heart attack (exceedingly rare, I know, but possible) that now requires an ICU admission, cardiac catheterization, echocardiogram, specialist consults, etc... tens of thousands of dollars of care or more. Most times, your insurance will not cover that since it was subsequent to cosmetic surgery.
There is a company or service I saw once (can't recall the name) that specifically offered coverage for just this scenario for plastic surgery patients.
The last issue that you raise is one of patient compliance. If a patient does not want to follow the doctor's recommendations, such as getting a CT, then it's probably best that the patient finds another doctor. Doctors don't get paid for ordering tests. We don't order them for our amusement. We order them when our clinical judgment suggests it's helpful in the care of the patient.
All the best,
--DCP

Hello!  Thank you for your question.  A CT scan is not completely necessary for a rhinoplasty, but your surgeon may be looking for something specific for surgical planning.  It will be up to your surgeon if he requires.  You should discuss with him/her.  Best wishes!

I think you may be confusing two different issues.
Surgeons rarely need a CT scan for a rhinoplasty. However, they frequently request it when contemplating a functional rhinoplasty in which the sinuses or breathing disorders are also being treated.
Plastic surgeons will not likely refuse your request but in this era of defensive medicine, they may request that you sign a document stating that you refused the recommendation.
If you are seeking to improve your breathing, then I would advise you to get a CT scan to make sure there are not other causes for your obstructive symptoms.
If, however, you want to only improve the appearance, then it is possible that a plastic surgeon would proceed without a CT scan