Finally, I got an idea to see if there are any male-to-female USB-C cables which would serve to extend the inaccessible USB-C port to somewhere closer to me so that I wouldn't have to crawl under the table with a torch.
This cable arrived today, and I tried it out. It works beautifully. Now, to switch I need to unplug and plug a single USB-C cable into whichever computer I want to use.
https://www.amazon.in/UGREEN-Extension-Extender-Nintendo-MacBook/dp/B08NTCD6VQ
I've also decided to hold off on the KVM switch, because I am almost certainly going to buy a Dell UltraSharp 27-inch monitor sometime in the future which has KVM features, making redundant the expensive KVM switch that I may have bought.
Such a relief. Sometimes, there are low tech solutions available, and doing something in a hurry can cause you to burn a lot of $COIN. These kind of setup issues are not easy/straightforward. It took me years to figure this out. I am a software engineer with 11+ years experience in the industry. 🙈