That still doesn't explain why Cloud removed his right pauldron.
Sephiroth is officially left-handed; he was right-handed in the first Kingdom Hearts, but officially, he's left handed in all other appearances, and thus if Cloud had to remove his right pauldron, Sephiroth would reciprocally have to remove his left pauldron.
Perhaps Cloud could have redesigned his outfit in some other way instead of removing his right pauldron, which leaves his right shoulder exposed.