The Hydra will work on the OSSC. But you should really consider if you need it and if it makes sense in your setup. You named three consoles:
1: The Wii needs a component cable to output the best possible resolution: 480p. These cables are common and cheap and if you look at your OSSC you will see that it has a component input – that means you can connect your Wii directly to the OSSC.
2: The Pal Gamecube doesn’t support Component 480p, so you are stuck hat 480i via RGB-Scart. But your Wii can also play Gamecube Games. They will still play only in 480i, but you can save some bucks here. Of course I understand that you probably still want to use the Gamecube itself.
3: N64 will not work.
In this case you only need 2 inputs and both are on the OSSC itself.
And again, I’m really sorry to disappoint you: The OSSC is a great devive, but it works best on Consoles with 2D-Content and 240p resolution, like the SNES or the Genesis. It will make the Wii look better, but even a RGB modded N64 with deblur won’t look good on your 65 inch TV. These early 3D-Consoles aren’t made for big screens. The same goes for the Gamecube, it has 480i output, which isn’t a problem on CRTs – but on the OSSC it will flicker and is just a blurry mess.