Common randomness arising from turbulence-induced signal fading in reciprocal optical wireless channels is a beneficial resource that can be used to generate secret keys shared by two legitimate parties. The concept of optical wireless channels using common-transverse-spatial-mode coupling (CTSMC) that can maintain perfect fading reciprocity in atmospheric turbulence is first developed in a general manner. Subsequently, by performing Monte Carlo simulations, the Johnson SB probability distribution is demonstrated to be appropriate for statistical description of turbulence-induced signal fading in an optical wireless channel constructed by use of two identical CTSMC transceivers, and the nature of correlation between signal fadings detected by two contiguous reception spatial modes is further quantitatively characterized, revealing that rapid spatial decorrelation between signal fadings observed by a legitimate party and an eavesdropper holds for scenarios of practical interest. Finally, the information theoretic capacity for generating secret keys from CTSMC-based optical wireless channels is theoretically formulated and quantitatively examined under different conditions, manifesting that the turbulence strength and average electrical signal-to-noise ratio have a noticeable combined impact on the secret key capacity, especially in the far-field case.