Does Switch current rating matters if its connected to ground wire
The ground wire is still part of the current loop so you need at least a 200mA rated switch.

That being said, don't put the switch on the ground line. If you do then parts of the circuit could still be "live" (at the potential of the power supply positive output with respect to ground) even when the switch is off. It would be much easier to accidentally short it out. Always put your power switch on the positive side of the circuit. This ensures that when the switch is in the off position the entire circuit is at 0V potential.