Be careful with SSR's. If there is not a sufficient load/current draw it will not switch.
I have noticed over the years that when SSR's fail they usually fail in the closed position. SSR's are great in the right application.
I think you can find a cube that has a higher rating than 10 amps. But I have not seen or used one.
You can use a miniture (IEC) traditional relay, Then you can choose the one with the correct current requirement.
