Those cables go the wrong way, they let you plug a serial device into a USB port.
Some (most ?) USB mice come with USB to PS2 converters (I have a couple lieing around the place I think). Why doesn’t this computer have a PS2 port ?
I don’t know the reason for this. I think the computers I’m refering to are workstations (not PCs) and the jack that is (apparently) for the mouse plugs into the keyboard. These jacks are 9-pin (DB-9?)
Buy a USB mouse it’s like a couple of bucks! Why buy out of date technology, go forward man. If you have run out of USB ports just buy a USB hub.
If you are keen on getting all these old ports I’d suggest going for a usb port replicator to give you extra usb ports, serial, parallel etc, and all on the one device.