Replacing your router with a multi-WAN router will accomplish what you want, I think. There are a lot of choices there.
Some of my favorites, lately, come from GL-inet. Something as simple as their Beryl AX might do the job, replacing your existing router with one that can be told, via its web-based UI, to use the amplified WiFi signal or Starlink as your WAN connection. Might not have the range to cover a 49-foot cat, though. They have higher-end devices that can do the same thing. They also have some with cellular modems, like the Spitz AX, that can let you choose between any number of WiFi, 1-2 wired connections, or a subscribed SIM card. IMO these devices are particularly user-friendly, though there is a learning curve similar to that of any home router. As a bonus, these gadgets come with a decent Wireguard implementation (if you're into VPNs) and Adguard Home, so you could eliminate ads for the whole boat pretty trivially.
The thing is, though, they're built for personal travel and/or home use and aren't exactly nautical in build quality. While I've never had one fail, I've also never taken one to sea. Some of 'em run on 5V. I currently have a GL-X3000 (Spitz AX) wall-mounted in our travel trailer behind the TV, and it runs fine on 12V. When we get where we're going, I spend a few minutes with its UI to select the best backhaul (in my case, between passively amplified local WiFi, either of two cellular providers, or Starlink), and then give my wife a thumbs-up.
On our boat I used a Peplink MAX BR1 Mini, which is a much sturdier-looking multi-WAN device that runs on 12V and can switch between WANs, and also up to two cellular SIMs. It is designed to be deployed in vehicles (mostly trucks, but as you can tell by this thread, they find their way into a lot of boats). The user interface is admittedly more a little more data-center oriented (powerful, steeper learning curve). They have pretty good tech support, though it is subscription-based. I've also used their Balance products, in other settings where no cellular is needed, but those seem to be all more expensive these days - you'd be just as well off with a BR1 and just not bothering about putting SIM cards in it.
I've also been experimenting lately with Mikrotik devices - they're product line is ginormous and inexpensive, and they've got quite a few gadgets with Multi-Wan, but the "RouterOS" software has the steepest learning curve I've seen yet (enterprise brands like Cisco and Juniper aside). Any of their recent products that has both wifi and wired ethernet connections will be configurable as a multi-wan router.
In your case, I think the search string "Can the (insert manufacturer here) (model name here) use WiFi as WAN?" is likely your friend. If it has that, you can probably replace your router with it and achieve what you're looking for.