I used to have regular shiatsu massages years ago (way before PD), and I loved it - it's very energising. Unfortunately it's difficult to find a practitioner now, otherwise I would definitely have more.
I say go for it, it can't do you any harm!
Swedish massage is wonderful but very different. I did the ITEC course in it many years ago so practised it for a while. It's great for improving circulation, relaxing muscles and getting rid of toxins.