Can't be done. The E4OD is operated by the computer.
The old C6 is self contained and controled by vacuum modulator.
To clairify, mechanically it could be done but the results, when all is considered, will not be very good.
The computer is expecting to see the transmission connected through the harness.
There would be a CEL lite on all the time with the codes set indicating no connection to the trans.
Emmisions, no overdrive, mounting, driveshaft, shifter linkage etc.
I think you would be worse off then if your unhappy now.
Tell more about the shutter and what has been done so far.
Shutter can be a number of things from fluid to clutches/bands, to lockup, to even computer program changes.
I have saw all these over many years of cars and truck.
I admitt that it takes a good trans man to work it out and those are sometimes few and far between.