Cell-Free Massive MIMO (CF mMIMO) has emerged as a potential enabler for future networks. It has been shown that these networks are much more energy-efficient than classical cellular systems when they are serving users at peak capacity. However, these CF mMIMO networks are designed for peak traffic loads, and when this is not the case, they are significantly over-dimensioned and not at all energy efficient. To this end, Adaptive Access Point (AP) ON/OFF Switching (ASO) strategies have been developed to save energy when the network is not at peak traffic loads by putting unnecessary APs to sleep. Unfortunately, the existing strategies rely on measuring channel state information between every user and every access point, resulting in significant measurement energy consumption overheads. Furthermore, the current state-of-art approach has a computational complexity that scales exponentially with the number of APs. In this work, we present a novel convex feasibility testing method that allows checking per-user Quality-of-Service (QoS) requirements without necessarily considering all possible access point activations. We then propose an iterative algorithm for activating access points until all users' requirements are fulfilled. We show that our method has comparable performance to the optimal solution whilst avoiding solving costly mixed-integer problems and measuring channel state information on only a limited subset of APs.