Both options presented can work. If you plan to leave the amps on, a switch will be required, but if you plan to enable signal output by turning the amps on and off, a signal splitter is all you need.
IMO you can get better signal quality through a quality splitter vs a switch. If you are running single ended / RCA, then consider these, which will allow you to run whichever RCAs you want vs a Y-cable:
https://silversonic.com/products/connectors/y-block-connector/