He could have used his pockets...
Would Cooper have tied the money bag and tied the full dummy chest chute to himself for few packets? There weren't D rings to properly attach.
If he emptied the dummy, why toss the contents.
Sure, he could have used his pockets. That said, we know he tried putting at least some of the ransom in a reserve. Makes sense that he stuck with his plan and put some of it in the reserve.
I do not believe he merely threw the dummy reserve out. After all, it's never been found. And, it would have been easier and safer to just leave it on the jet. In my mind he took the dummy reserve for a reason...securing a small portion of the ransom makes sense.
The contents of the dummy remained in the dummy. Why? Because if he removed them...which would have involved a lot of additional effort and cutting...it would then mean the dummy reserve had too much space inside. In fact, the bundles would have been tumbling around. Again, it makes sense to cram in a few packets (3,4, 8...whatever) into the dummy reserve. Also, the shroud lines in the dummy could have been used to repel from a tree if DBC landed in a tree (Sheridan discusses this in his book).