Cable modems pull the signal from a coax line and turn it into an ethernet signal that comes out of a single RJ-45 plug.
I dunno squat about what goes on inside of those boxes, but routers typically have a WAN port and a bunch of “internal” ports that are all RJ-45 plugs.
If you can get Cox to send traffic for a group of IPs to your modem, then they should all come out the ethernet side as well, right?
Remember that their modem is NOT a “router”. You can plug a router into it, tho.
On using openwrt on legacy routers, start here, find anything that is *well* supported and hunt on ebay, or go to a thrift shop and search this list if you find a decent looking box. At one point years ago I'd scooped up several decent goodwill routers for some $5-7ea and flashed to openwrt to give to family and friends when they complained about their crappy router and wifi not working. Probably still have one or two floating around...
-mb