There are two types of tremors --- intention tremors (occur or worsen with activity) and rest tremors (present at rest, relieved by activity). Typically PD is a rest tremor, essential tremor is more intention, but these rules are not hard and fast, so most neurologists do not place much emphasis on this distinction any longer.
Unilateral tremor is more often PD, bilateral onset is more typical of essential tremor. Tremor of the voice or head is rare with PD, common with ET. Alcohol relieves ET, not PD, but doctors should NEVER recommend alcohol to control tremor. A trial of a beta-blocker is better.
Treatment for PD should be initiated when the symptoms interfere with daily life, although there is some animal data suggesting that dopamine agonists like Requip slow the progression of the disease. Thus, some neurologists advocate their use early on...also, taking the vitamin Coenzyme Q has been shown to slow the disease in some models, but this remains controversial.
I believe that the dive medicine community feels that PD, like MS, is such a variable disease that no broad statement about PD and diving is possible. It's a case by case thing, and in this case, untreated unilateral tremor in an otherwise healthy active person should not a contraindication to diving IMHO. I've been diving for years with such a tremor. And no dive op has given me grief about it...plus, unlike heart disease, it's not something you can lie about or hide. Because PD tremors do tend to improve with activity, they are often more cosmetically challenging than they are debilitating...in fact, ET can be more debilitating than early PD, even though PD has more long-term problems than ET.