Coded caching was introduced in partially cooperative D2D networks where some selfish users keep silent during delivery process. In existing works, unselfish users were randomly selected as delivery proxies for selfish users, resulting in asymmetric utilization of unselfish users. We observe that averaging the transmission load uniformly over unselfish users may achieve better performance. With this motivation, we propose scheme A, which symmetrically employs all unselfish users in delivery, and its transmission rate outperforms the schemes in existing works. Moreover, existing schemes applied the same symmetric cache placement and file splitting strategy as in the fully cooperative D2D networks, which ignored the asymmetry brought by the silent selfish users and thus incurred extra transmission. Consequently, we propose scheme B with an asymmetric file division strategy where the subfiles are exclusively designated to be sent by unselfish users, thus eliminating the proxy transmissions. To evaluate the performance of proposed schemes, a new converse bound is derived by the index coding approach. The joint performance of schemes A and B in certain regime is shown to be exact-optimal under uncoded placement when S = 1, where S represents the number of selfish users. Similar to existing works, schemes A and B require an assumption that S ≤ t − 1, where t represents the caching redundancy. When S ≥ t, we further propose scheme C employing uncoded placement, which outperforms the existing MDS-code based scheme in certain regime due to reduction on coding overhead. Numerical simulations are conducted to verify the superior performance of the proposed schemes.