Yes, you can use a SSR to switch in any polarity just like a normal switch/relay
But make sure you order a DC SSR not an AC SSR (if it says zero crossing or not-zero crossing its AC)
If it says AC/DC that's fine, it can do both.
The SSR gets power from light that is generated by the IR LED built inside.
You control the LED and this puts light onto a tiny solar cell which turns on two fets (two are used so that it can block/pass current in both polarities).
As soon as you cut the power to the LED the switch stops passing current in either direction.
Obviously you have to pay attention to the SSR specs for max current/voltage and max LED current etc..
Also the SSR may pass a very tiny bit of 'leakage' current when switched off, but this is usually too small to be of any concern.
Some SSR's have the current limit resistor for the LED built in, some don't, so check that.
It's an IR led so its forward voltage is around 1V.