You are looking for a “dual WAN router.” The TP-Link ER605 v2 (don’t get v1) might be a good option for you. B&H Photo is a better seller than Amazon to ensure you get the v2. It is wired-only, so you’ll need something else to cover your wireless needs. Your existing router may work fine as an access point.
I can’t see your photo, but I think multi-cable staples are what you’re looking for.