Power loss in an RC circuit with very low resistance
If you are trying to charge a capacitor via a resistor from a fixed voltage DC source then the energy you lose (to heat) in the resistor is always the same irrespective of how large or how small that resistor is. The charge time (as dictated by RC) is irrelevant to the problem.

You don't need to worry about EM radiation as a factor in order to to prove this i.e. you can assume there will be no radiation other than as heat from the resistor.