Static means that it something move or change. So when you move the body, Chipmunk won't update any shapes attached to the static body unless you use one of the cpSpaceReindex*() functions to let it know that it needs to.
The better solution is to use a "rogue" body. Create a body, but don't add it to the space. Chipmunk will update it's shapes each frame like normal (they are separate objects), but it won't update the body's position or velocity automatically.
Also, if you set a body's position each frame, you should also set it's velocity to match. Otherwise you are going to end up with mushy, non-realistic collisions. If you want to do mouse control, you may also want to look at how the Chipmunk demo implements that using joints.