Hi,
just to be sure: resolution is 1 microohm or 1 milliohm?
The current shunt is not that big problem, because you have equal temperature at he joints, so ideally the thermocouple effects will cancle itself.
The bigger problem is the voltage measurement at the DUT. Here the voltages might be much smaller than at the shunt and the temperatures are not predictable.
AC excitation is not that problem.
I´d use some H-bride configuration with MOSFETs. the gate currents are negligible and the voltage drop is no problem. Low voltage types (<20V) with Rds-on of a few mohms are easy to find.
Switching speed is no problem, power loss is also no problem.
If you need precision, then do it with AC.
software is important, too. But that after hardware is finished.
Klaus