Small wireless transmitter and receiver
Transmitters do not have access to microcontroller

Without some kind of brains behind the transmitter, &quot;collisions&quot; are guaranteed.  ((All)) multi-user environments, from old party-line telephone systems to 5G, require brains behind the transmitter to recognize and recover from whatever form of collision/over-talking/garbled transmission that has taken place.  A key requirement for this is that each transmitter must have a receiver, either to be told when to transmit, to to be told to re-transmit the last message.
Examples of those two options are more popularly know as ARCnet (a form of token ring) and Ethernet (CSMA/CD - the CD stands for collision detection).  You don't need anything that complex for a small, low speed, dedicated system.  But note that Bluetooth and BLE both are bi-directional systems with collision handling built into their communication protocols.