I think noise is preferible than motion blur. It is easier to remove anyway.
For this particular case you are asking I would explore this tools:
1) A morphing program like photomorph (free). I'm not sure about dimension restrictions. You probably need to re-asign the background in case it is deformed too.
2) Photoshop has a wrap grid tool (Edit > Transform > Warp), I think a little limited (at least in my oldy version). Work in layers, make them semitransparent to see the reference, and use small selections.
3) The liquify tool in Photoshop. The problem here is that you don't see what is in the other layer. I would use a transparency tool. For windows there is one called Glass2k. The workarround would be running 2 instances of Photoshop.
4) If you don't have sharp edges there probably the smudge tool can help.
But probably an easier way is to use the stamp tool or just to make transparent one layer in some specific spots. Yeap you would have some not eliminated noise, but if you say it is on a small area, probably nobody will notice it. Of course you can retouch that small noisy zone with a blur tool.
Another kind of double exposure
There is a technique I still have to explore that is taking a dark picture to capture only noise and subscract that from a real shot. Sounds interesting.
Try this noise removal tool: http://www.neatimage.com/ Actually there is an option there to find the noise pattern of your camera and use it to remove the noise.