4 watts per thinsat - and 10 milliwatts per chip - is not much power. Calculations are "radiation targets", but logic that is unpowered is not subject to single event upsets (SEU). If most logic is unpowered ("dark") most of the time, then it is only vulnerable to SEU when it is turned on.
The server sky design philosophy will be hard-wired logic, not instruction streams and general purpose CPU, for all the tasks that can confidently be implemented hard-wired. This could be image rendering, kilobit integer cryptography, radio calculations. Integer calculations can be performed in parallel, in high and low precision (modulo-small-prime, "woop" verification), and if the modulus of the large calculation does not match the small one (perhaps due to a SEU), it is repeated.
We will not have the mass budget for big capacitors, but very small capacitors may permit ten microsecond bursts of calculation spaced a millisecond apart.