Hi,
in electronics design we use specifications, like: Volts, amperes, frequency, waveform, ohms ...
I don´t find any specification. Thus - for me - it´s impossible to give any recommendation.
Oh, I´m wrong, there is a specification: it says "1k". But nothing about the input voltage, nothing about the diode current (which should be a LED, I guess)..
In SSR´s there is no functional electrical connection between "control" and "load".
But analog switches and FETs refer to the same voltage system (you may call it GND). Control and load are not galvanically isolated.
As long as you don´t provide informations about your application it´s impossible to decide whether a FET or an analog switch is suitable.
Klaus