sadly all the evidence got burned so he might not be able to convince her. In the unstable condition she was in, explaining things to her won't be enough sadly.
Cid and Sherry are strangers, Cid has no emotional or any other form of obligation to her whatsoever and prefers it that way, the moment he does that he'll be in a relationship with her and the harem will be for real. He trimmed the fat so he's devoting himself to his principles and ideals.
Sherry herself cannot ask for anything more from him as they 'just' became 'friends' as well.