Uplink ultra-reliable low-latency communication (URLLC) entails dependable and almost instantaneous packet transmissions from industrial Internet of Things terminals to the serving base station. While most of the literature addresses terminals which are always connected to the network, here we focus on terminals which would benefit from a connection-less radio access, because they are employed for low-duty-cycle applications related to industrial safety, while still requiring a URLLC quality of service. Our aim is to investigate the performance of two standard-compliant radio access protocols, i.e., the one-stage approach and the two-stage approach, in supporting uplink URLLC in connection-less mode. We derive a mathematical model of these protocols under the assumption that the base station has multi-user detection capabilities. The model is used to cross-validate our simulator and calibrate the protocols together with the validated simulator, providing well-grounded guidelines for the selection of the parameter values. The simulator is finally exploited to assess the URLLC performance of the proposed protocols. The key outcome of this study is that, when combined with multi-user detection at the base station and after an appropriate system parameters selection, the one-stage approach satisfies the desired URLLC service requirements, thus representing a viable solution to support safety-related industrial applications.