Composed of two pieces. One (the square like) plugged into one end and generates a tone. The other piece is a probe that can sense the tone when it's needle is placed on the cable, the tone is converted to a buzzing/beeping sound that you can hear to find the cable.
Yes it will work but if you use it without a probe (the TC-TP1), you will have to connect the 2nd side to each and every cable until you find the one. Since the cables are few then I don't think it will be a problem. But if you had more than like 50 cables it can become tedious.
There is another cheaper idea if you want. First disconnect all PCs/devices from the wall connections (while keeping the switch side connected). Then take a laptop, connect it to the first node, go the switch and check what led port goes up. You got the first one. Connect the laptop to the second node, go to the switch, check the port. And so on until you do all nodes. Does this make any sense?