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!

Some insurance companies have required scans for preauthorization which is ironic because the scan costs almost as much as they pay in network doctors. This is probably part of a plan to deny payment or to create such difficult barriers to surgery that patients either give up or pay out of pocket.