OP can perform rbf as long as the transaction he made is flagged as rbf even if he doesn't have access to wallets which made the parent transactions (someone corrects me if I'm wrong!).
When replacing a transaction by fee, you are telling the node to remove it and replace it with a new one which consumes the same (or a single) inputs and pays higher fees. Technically, this doesn't affect or introduce any change to the parent transaction(s).