As a natural hygiene purist, my first reaction to oil pulling on a water-only-fast would be most definitely not, but I have become open-minded enough over the years (hopefully) to examine all things.
In your case I would say yes, please go ahead with it, as you have so many health problems.
Some would say (including myself for many years) that by stimulating saliva you are therefore initiating the digestive process and breaking the fast, but in reality, unless anything is introduced into the stomach directly, this simply just isn't the case.
So yes, I would say go ahead with it, but it will take time.