"It's quite difficult, and requires a lot of energy to liquefy H20"

Looking at this again it seems that what you meant was
liquefy H2 and O2.

This could be a problem, but there are some things which
could make this fairly easy.
One thing, is one could arrange the 200 tons of water,
so they are between your radiators and Earth. In addition you use your solar panels to shade the radiators from the sunlight.
I order to refrigerate the H2 and O2 you need to pressurize these gases, and pressurize them enough so the gas is warmer than the environment- the greater the difference
the faster you lose heat.
Said differently the environment needs to radiate less heat to radiator than the heat radiated from the radiators.
If the radiators are shaded from Earth and from the Sun. then one would need to pressurize these gases less.

So you could a situation where the warmest objects which heating the radiator is the water tanks- and say the water and the tanks are 70 F [you could have them even colder- by simply shading them].

So imagine being nowhere near the sun, and having a object which warmed "somehow" so it's 70 F, you have another object which is 10 or 20' away and it is only warmed by this 70 F object. How cold does this second object get- space has a background temperature of something like 3 K.

Now if your radiating object is 100 C warmer than the radiation received- it should radiate a fair amount of heat.
But if you only trying to cool 20 tons per year- or 1.7 tons per month, .4 tons per week, .06 tons per day, you don't need to radiate very much heat.
Of course if you need to cool 100 tons per year it's a bit more difficult.