Do I need to prove this?
I purposefully did not look at the details of the change you are proposing because whatever the change is, the answer is a resounding YES. If you make any change to a cryptographic construction, then you must prove the security of the modified scheme. If you are lucky, you may be able to reduce the security of the modified scheme to the original scheme, or you may be able to reuse a lot of the intermediate claims of the proof of the original scheme. However, you must prove!