Is it possible to to wrap or cut a wood moulding around a stair nose?
No, but there is a quick and easy solution which provides the look. Use a panel moulding from the #311 series, mark a line about 8-9″ on the side wall (Skirting) above every stair nose from the top of the staircase to the bottom, attach the moulding #311 on this line, paint the moulding and the wall a color different from your main painted wall, now it gives the appearance that there is a skirt panel running up your stairs. If there are slight gaps between your nosing and the wall use a paintable caulking to bridge these gaps.