What is the best way to parallel two shunt resistors using a switch?
The lowest on-resistance switch is likely to be a MOSFET. Various manufacturers make them, and some have on-resistances as low as 1mΩ.
This will introduce some error in the measurement.  A 1mΩ on resistance would increase the resistance of the combo from 50.0mΩ to 50.5mΩ.
I would agree with the comment by Transistor though. While this should work, there is probably a better way to do whatever it is you are trying to do with this design.