Why would a vascular study be recommend to me, by surgeon, for chronic idiopathic peripheral neuralgia/neuropathy and pudendal neuralgia.

Evaluate vasculature: while a vascular study is not complete enough to fully determine the cause of nerve damage it can rule out a vascular abnormalities. Ultimately a nerve study such as an EMG will be necessary. In addition an MR I of the spine and pelvis might be considered.

To Rule Out Ischemia: I am not certain why the test was ordered, but suspect that it may have been an attempt to insure that you are not suffering from peripheral vascular disease--which can mimic some of the symptoms of a peripheral neuropathy/neuralgia.