This paper studies cell-free massive multiple-input multiple-output (CF-mMIMO) systems incorporating simultane-ous wireless information and power transfer (SWIPT) for separate information users (IUs) and energy users (EUs) in Internet of Things (IoT) networks. To optimize both the spectral efficiency (SE) of IUs and harvested energy (HE) of EUs, we propose a joint access point (AP) operation mode selection and power control design, wherein certain APs are designated for energy transmission to EUs, while others are dedicated to information transmission to IUs. We investigate the problem of maximizing the total HE for EUs, considering constraints on SE for individual IUs and minimum HE for individual EUs. Our numerical results showcase that the proposed AP operation mode selection algorithm can provide up to 76% and 130% performance gains over random AP operation mode selection with and without power control, respectively,