No, I may have expressed myself somewhat awkward, leading to these misunderstandings.

I'll explain more in detail:
This is my setup: coax cable -> cable modem -> ethernet cable -> into WAN port of (wireless) router -> from LAN port of (wireless) router -> to 24 port gigabit switch -> to all ethernet wall connections.

If I put the router upstairs as you suggest, then I separate the modem and the wireless router from the same room. This in itself is not a problem, since I have an ethernet cable running up to that room. (so I can connect the router, and I would have good wireless connectivity)
BUT... once the router is connected, I also need an ethernet cable coming back down from one of the LAN ports of the router to the technical room again, to connect into the 24 ports switch.

It's that second cable that I'm lacking. Bitt's suggestion would solve that problem, as would a smart switch using VLAN's. Unfortunately Bitt's solution would slow down my internet connection and adding a smart switch would cost more than just buying one of those TP-link routers, configure it as an access point and be done with it.