Controlling low wattage SMPS with SSR
I don't know how the minimum current specification of the SSR will affect the operation of the power supply. 


This should be OK.

The SSR leakage current spec of 3.0mA max at any rated voltage, which implies for 240Vac a power leakage worst case of 720 mVA. This may charge up the input caps to some voltage and may be unsafe to touch the input voltage but is unlikely to cause any damage. 

The supply has a leakage to the PE ground spec of 2mA max which is for the Y cap filters.