This paper investigates the impact of a uniform circular array (UCA) in the context of wireless security via exposure region-based beamforming. An improvement is demonstrated for the security metric proposed in our previous paper, namely, the spatial secrecy outage probability (SSOP), by optimizing the configuration of the UCA. Our previous paper focused on formalizing the SSOP concept and exploring its applicability using a uniform linear array example. This paper proposes the UCA as a superior candidate because it is more robust against the effects of mutual coupling. The UCA's SSOP configuration is explored and a special expression is derived from the general expression for the first time, and a closed-form upper bound is then generated to facilitate analysis. By carefully designing the UCA structure particularly the radius, an SSOP optimization algorithm is derived and explored for mutual coupling. It is shown that the information leakage to eavesdroppers is reduced while the legitimate user's received signal quality is enhanced due to the use of beamforming.