This paper presents a strategy for using an external microphone for enhancing noisy speech in single-microphone completely-in-canal (CIC) hearing aids. The external microphone is placed such that it benefits from the body shielding noise from the back hemisphere. The presented algorithm first enhances the external microphone signal without assuming an exact known location of the external microphone. The proposed algorithm then automatically incorporates the enhanced external microphone signal for post-processing enhancement of a conventional dual-channel binaural beamformer whenever the external microphone has a significant SNR advantage. The overall enhancement scheme avoids error-prone estimations of target voice activity detection and relative transfer functions between the microphones. Unlike single-channel post-processing filters which are limited to reducing stationary or diffuse noise, the proposed post-processing filter is able to reduce highly non-stationary directional noise from the back hemisphere. The resulting system provides enhancement even for noise arriving from the backward direction, which conventionally is difficult for CIC hearing aids where there exists a front-back ambiguity.