A SSR could work, but is probably overkill. You can use a SSR like a mechanical relay where you are using a small signal to switch a larger one, or a DC signal to switch AC. In your case a BJT or FET is cheap, simple and will do the trick. SSRs usually use some combination of FETs or TRIACs, depending on the application. In some cases, they can also isolate the signal and load, but that probably isn't a concern in your application.