A couple of points to note with your plan.
Although you could pay to go private in an NHS Hospital it would not be any cheaper than having it done in a Private Clinic.
The Private Clinic will Probably be a lot cleaner than your local NHS Hospital.
In a Private Bariatric Clinic all the staff will be trained to deal with Bariatric patients in an NHS Hospital it might just be the Surgeon and what about the Anesthetist, how many morbidly obese patients has he put under safely in an NHS Hospital, where they normally refuse to do surgery on obese patients.
Sorry not knocking the NHS which does a good job most of the time, but if I was paying for it I would want the best I could get for my money.
I am sure even in Scotland there are quite a few Private Bariatric Centres with extremely competent surgeons and nursing staff.
Paul