Is it possible to change the line style used for the element edges in a wireframe/shaded view of the meshin ABAQUS?

Yes its possible to change the line style used for drawing the element edges. Click on the Common Plot option icon (the first one first row and the one on the left to the left of the viewport).

In the dialog box which opens choose the Color & style tab. At the bottom there are 2 boxes with lines. The first one controls the line style of the edges of the elements in the mesh. Click on the scroll bar next to this line and choose a different line style.
Click on OK and this should change the appearance.