Is it possible to adjust the degree of perspective in the Perspective view display?
Yes. Activate the Perspective display mode in the part or assembly (use the icon or View - Display - Perspective). Now choose View - Modify - Perspective.... You have the option of adjusting the observer position. You can set the position to be from 0.001 to 1000 "object sizes away". Smaller numbers will show more parallax. The default value is 3. This is a document specific property.
SolidWorks 2006 introduced the ability to define cameras in a model. Go to View - Lights and Cameras - Add Camera, or right-click on the FeatureManager where it says "Lights and Cameras" and choose Add Camera. The camera controls give you more flexibility to define the degree of perspective based on Field of View settings. Camera Views are also the only way you can place your obeserver position to be inside your CAD model, lookout outward.