The 100m constraint is a very old constraint. At the time, it was a design decision for 10BASE-T.
IEEE could have used a larger distance (say 500m like 10BASE5 or 185m like 10BASE2), but then all the equipment that would implement 10BASE-T (cables, repeaters, NICs, bridges, etc) would have to be more sensitive and capable (translating to being more expensive). A basic tenet of the IEEE 802.3 Working Groups was that Ethernet had to be cheap. Cheap meant smaller distances. And to further lower costs, the cable type and characteristics that the 10BASE-T working group had to select had to be easy and streamlined to installa (lower training for installers, lower breakage during installations, more durable cabling).
After a compromise was made between usefulness (a 100m physical link is quite useful) and expected price per NIC/cable, the standard was written around that.
Another piece of baggage that 10BASE-T had to carry was the MAC sub-layer constraints of older Ethernet standards. (Ethernet frame format, minimum and maximum frame lengths, Inter-Frame Gap, etc)
The actual timing constraints of 10BASE-T (for CSMA/CD to function) came from older standards.
After the Working Group had concluded on a maximum distance, all they then had to do was define the cabling's minimum characteristics.
To find the minimum length, as defined by the standard, I believe you must study the IEEE 802.1 standard itself. I have seen references to a 2.5m minimum distance between 10BASE-T nodes, but I am not sure if this restriction is written in the standard. I know for a fact that with newer standards' implementations I have used 0.5m patch cords without any issues, but only on Ethernet point-to-point links.
But I noticed a weird phrasing in your question: you are asking about cabling between an end-device and a switch, and whether Collision Detection will work. Unless you are using a hub or a bridge (a very old device type), you should not be even able to produce collisions in this connection.
So, to answer your question "what is the minimum cable length (or minimum segment length) between end device and switch, so as to ensure Collision Detection works during Half Duplex operation", the answer is:
It's an impossible question to answer. You cannot get a Collision on a device connected to a switch with a UTP cable. You need something else that creates a shared medium somewhere. So, no, there is no minimum length of cable that will allow collision detection to work on an end-device or a switch directly connected to each other with a UTP cable.