That you are suggesting more than 1 port makes me think you have more than one device. It is possible to go from a cable modem to one single computer (at least some modems) with nothing but a RJ45 cable, but if you have more than one device you need Network Address translation which is rarely if ever found in switches, even layer 3 switches.
One option is just get a wifi router and set the password to something long and then forget it; if you can set SSID not to broadcast and it will be mostly invisible. I was a bit surprised to see I could not turn off my radios on my GUI (I use DD-WRT which gives you a LOT of settings). I am sure I could do it at the command line, but indeed maybe you can't turn off most router radios. And some antennas can just be unscrewed (some risk of radio damage if you care) which would vastly limit their power if you are doing this to avoid EM fields or some such.
Another option is a more commercial device such as a firewall or "VPN Router". Maybe a low end used Cisco ASA for example. A problem with these is they really need to be kept up to date, and you may have issues getting current software cheaply as most are not free updates. But certainly non-radio routers exist, they are just usually higher end and more expensive. They may not always be called routers, most firewalls and "vpn gateways" and similar can do what you want, though it may take some research to make sure. "Network Address Translation" or "NAT" are good keywords to get started.
But honestly if you are doing this to avoid the cost of wifi -- it's probably cheaper with.