I know smoking is bad for a FUE hair transplant, but is it the nicotine or the actual smoke that is most harmful?

Smoking is not generally recommended after surgery.  If you are concerned it is best to check with your doctor or quit smoking.Nicotine itself is not the issue.

Smoking decreases blood flow to the scalp by constricting blood vessels. This means that less oxygen is delivered to the scalp because of the higher level of carbon monoxide in the blood. This may have an impact of obtaining optimal results following a hair transplant. While many smokers do get a successful outcome it is never recommended to smoke following any sort of procedure.To answer your question nicotine affects the oxygen level but from an overall perspective Ecigs are believed to be safer than cigarettes.However you should avoid smoking altogether for general health reasons.

In a hair transplant, the vascular restrictive properties of tobacco as well as many other ingredients in cigarettes can lead to blood flow issues that can cause a diminished supply of blood to the newly transplanted grafts. Hair follicles need good blood flow to grow new hairs.
It is best to quit smoking entirely . . . for many reasons. But if possible, it is very important to not smoke for at least a few days before surgery as well as the first two weeks after a hair transplant. This will give the grafts enough time to heal properly. It is also important for the patient to be aware of the possible risks associated with smoking and the possibility of less than ideal results for a hair transplant.

smoking constricts the blood vessels and therefore there is less blood supply to the transplanted hair. It both effects the growth rate and the result. 

Both the nixotine and the tars from cigarettes are harmful to the blood supply ti the scalp. e-Cigs are better especially if you have a low nicotine content in them