If e-cigarettes contain nicotine then they need to be stopped prior to surgery. Nicotine causes a release of epinephrine thus causing blood vessels to shrink down in size. Increasing your risk of wound healing problems.
The reason smoking increases risks with surgery is not because of the cancer causing agents, but rather the nicotine in the smoke. Nicotine causes blood vessels to constrict, decreasing blood flow, and increasing risks of surgery. Therefore, any product with nicotine is harmful to recovering from surgery. Thus, I tell my patients no cigarettes, no patches, no e-cigs. These are all nicotine delivery systems.