The relays you have should indicate a few things.
1- the primary or coil voltage is what is required to make the relay "change state" or "turn on". If they are 12VDC then you will need a DCSSR with a 12VDC power supply. If it is 120VAC then you can use a standard SSR.
2- the secondary (or contacts) should tell you how much current they can handle at VAC & VDC.
I always use 15Amp relays but that is because I have them kicking around.
If you have a good multimeter you can use it to check how many Amps the trigger is asking for. I have seen 2 different characteristics with different Foggers. Some use the switch to control a relay for the fog release (which takes minimal current) but others seem to run the fogger through the switch (I've seen 8Amps on one of my old ones).
As you say, at least there is time to play.