This is how I deal with shadows when shooting a panorama with a monopod.
I use a Nikon D300, Sigma 8mm f3.5 lens, Nodal Ninja Ultimate R1 head (tilted up 5 degrees),  Manfrotto monopod and a Manfrotto spirit level that clamps onto the monopod shaft.  It took me about 10 panoramas before I finally figured out a sequence that works 99.9% of the time.        
I start with my back against the sun, behind the monopod.  This throws my shadow into only 1 picture.  The camera is just at my eye level.  With the sun at such a low angle, the camera shadow appears above my head.
I then proceed to take the rest of the sequence at 90 degree steps.  My shadow appears only 1 time in the center of the first frame.        
When I finish taking the 4th picture, I am standing with my shadow off to my right side.  Keeping the monopod in the same place I step back about 2 feet.  I remove the camera from the monopod with my right hand, rotate the camera down and away from me so I can see the bottom of the camera. The back of the camera is facing up at the sky.  I rest the camera on the monopod in order to help me set the camera at the same height it was during the previous 4 shots.  I make sure the monopod is still positioned straight and plumb.  I then check that the camera is as level as I can get it before removing the monopod with my left hand. With the monopod held out of the picture, I snap the 1st Nadir patch shot..

When the camera is flat and level, the plastic LCD shield is almost eye level for me.  I use this as a was to tell if I am holding the camera in the correct position before taking the Nadir patch shots.

If I am in the correct position, the shadow of the camera out at the end of my arm will overlap the shadow of the camera in the very first shot of the sequence.  This creates an area of overlapping shadows and will not allow for a fully patched Nadir shot.        
To solve this, I take a second patch shot.  I keep my eye on the camera shadow.  I move my arm back until I have a clear shot of where the camera shadow was and take the second patch shot.        
Draw a line from one of the dark spots in the center of the picture up to the light post.  You can see that I moved in more than 1 direction, so the perspective is not absolutely correct.  The important part of the 2nd patch shot is the area right around the camera shadow.  The rest of the picture will not be used.        
Bring both patch shots into Photoshop.  Using the second Nadir patch shot, remove the camera shadow from the 1st one.        
Looks like my arm is cut off.  That is what you want.        
I use an Alpha channel mask to exclude the areas of the picture I no longer need.        
Apply an Alpha channel mask to the 1st shot in the sequence        
Bring it all into PTGui and stitch away!        
Here is the panorama without any patching.        
Here is the completed panorama without any pesky photographer shadow.         
For very low light conditions, instead of removing the monopod from the shot, I put the bottom of the monopod on the ground about 2 feet away from the center of the picture, lean it way over so I can rest the camera on it and still get a clear Nadir patch shot.  Although not perfect, I have found that you can steady the camera good enough to use very slow shutter speeds.        
The technique will probably work with a tripod, but I have not tried that yet.