Time-Sensitive Networking (TSN) aims to extend the IEEE 802.1Q Ethernet standard with real-time and time-aware capabilities. Each device's transmission of time-critical frames is done according to a so-called Gate Control List (GCL) schedule via the timed-gate mechanism described in IEEE 802.1Qbv. Most schedule generation mechanisms for TSN have a constraining assumption that both switches and end-systems in the network must have at least the TSN capabilities related to scheduled gates and time synchronization. However, many TSN networks use off-the-shelf end-systems, e.g., for providing sensor data, which are not scheduled and/or synchronized. In this paper, we propose a more flexible scheduling strategy that considers a worst-case delay analysis within the scheduling synthesis step, leveraging the solution's optimality to support TSN networks with unscheduled and unsynchronized end-systems while still being able to guarantee bounded latency for critical messages. Our method enables real-world systems that feature off-the-shelf microcontrollers and sensor nodes without TSN capabilities connected to state-of-the-art TSN networks to communicate critical messages in a real-time fashion. We evaluate our approach using both synthetic and real-world test cases, comparing it with existing scheduling mechanisms. Furthermore, we use OMNET++ to validate the generated GCL schedules.