This question only makes sense on Windows, because if your computers were running macOS or Linux, the operating systems already provides all MIDI routing and connectivity functions out of the box. As it should be, because that is the point of MIDI since the beginning: to be able to connect any MIDI source to any other MIDI receiver. Musicians were asking for this feature 30 years ago, and MIDI was born to provide it. But there was nobody listening in Redmond then, and neither there is now.

Answering your question like "Any DAW will do that; try Cakewalk for instance" will probably be wrong, because you explicitly said "a simple software", and certainly Cakewalk is not simple. But then, the function you want is so extremely simple to implement that any program including it probably does something more.

One classic Windows utility is http://www.midiox.com/ but I don't know if it would work in your scenario, because it is a 32 bit program designed for Windows XP. A modern alternative is https://blog.veles.rs/midi-router-tool/ .

You may also use my VMPK software as a midi router (there is a checkbox in the MIDI connections dialog labeled "Enable MIDI Thru on MIDI Output"). But in this case, If you have both computers connected to the same local network, I would recommend you to try https://sourceforge.net/p/vmpk/wiki/MIDI%20by%20Network/ instead of using a MIDI cable between both computers.