Small footprint embedded devices require keyword spotters (KWS) with small model size and detection latency for enabling voice assistants. Such a keyword is often referred to as \textit{wake word} as it is used to wake up voice assistant enabled devices. Together with wake word detection, accurate estimation of wake word endpoints (start and end) is an important task of KWS. In this paper, we propose two new methods for detecting the endpoints of wake words in neural KWS that use single-stage word-level neural networks. Our results show that the new techniques give superior accuracy for detecting wake words' endpoints of up to 50 msec standard error versus human annotations, on par with the conventional Acoustic Model plus HMM forced alignment. To our knowledge, this is the first study of wake word endpoints detection methods for single-stage neural KWS.