Traditional communications focus on regular and orthogonal signal waveforms for simplified signal processing and improved spectral efficiency. In contrast, the next-generation communications would aim for irregular and non-orthogonal signal waveforms to introduce new capabilities. This work proposes a spectrally efficient irregular Sinc (irSinc) shaping technique, revisiting the traditional Sinc back to 1924, with the aim of enhancing performance in industrial Internet of things (IIoT). In time-critical IIoT applications, low-latency and time-jitter tolerance are two critical factors that significantly impact the performance and reliability. Recognizing the inevitability of latency and jitter in practice, this work aims to propose a waveform technique to mitigate these effects via reducing latency and enhancing the system robustness under time jitter effects. The utilization of irSinc yields a signal with increased spectral efficiency without sacrificing error performance. Integrating the irSinc in a two-stage framework, a single-carrier non-orthogonal frequency shaping (SC-NOFS) waveform is developed, showcasing perfect compatibility with 5G standards, enabling the direct integration of irSinc in existing industrial IoT setups. Through 5G standard signal configuration, our signal achieves faster data transmission within the same spectral bandwidth. Hardware experiments validate an 18% saving in timing resources, leading to either reduced latency or enhanced jitter tolerance.