Sounds more like essential tremor than parkinson's, especially if you're young and it hasn't really changed in ten years. But better see a doc to be sure. Once you get the cause identified, then go see the AME.
The AME, not the CFI or DPE, will determine whether it's disqualifying. It sounds like it would not be a problem.
The DPE/CFI can't disqualify you because you have a tremor, they don't get to pass judgement on that. They have to evaluate you on your performance only, worst case they might ask you to see an AME, but if you've already done that, then no issue.
Note... if you have a previous history of medical care/diagnosis for this and did not report it to the FAA when you applied for medicals, contact a lawyer before you do anything else.