new quaker appears to be quite itchy

Welcome to you and your new QP. There are many possibilities about what could be making your parrot itchy. Does he have lots of new pin feathers coming in? That's a major cause of a parrot picking at feathers. Parasites are a possibility too, and there's an off chance of an underlying illness. If you haven't already done so, scheduling a visit with a veterinarian experienced with taking care of parrots would be a good idea. Avoid using anything meant for treating parasites unless provided or recommended by a qualified veterinarian. A bath would be a good idea too. If you have a good clean spray bottle (one that never contained household chemicals, soap or cleaning agents) you could try misting your Quaker parrot. You might also try providing a shallow pan or dish of water to see if the parrot might bathe on his own. Hope that your new feathered friend settles in well with you and you enjoy a good life together.