I am guessing that you would get reasonable values by soldering a thick copper wire along the entire length of the side of the PCB connected to the current source, then an extra sens-wire to the DMM.
Perhaps, but I wasn't keen to try, I think the results would be quite muddy.
...
I took your statement as a challenge, I hope you don't mind
With just handheld multimeters and a homebuilt power supply I had at home, I decided to prove that it would not be hard to measure the resistance of the square of copper on a PCB (0.036 mm thick). However I did not have any empty PCBs at home so I had to use an even more difficult "sample". A sheet of 0.1 mm thick pure Silver, which would have only ca. 30 % of the resistance as the PCB!

0.0001 m thick Silver with a resistivity of 15.87 [nOhm m] would have a sheet resistance of only 0.0001587 Ohm/sq, that is only
158.7 uOhm/sq.!
Challenge Accepted!
I made a 17 mm by 17 mm square of the Silver sheet and soldered a 0.75 sq.mm copper cable along the length of two sides. Then I soldered thinner sense wires on the opposite side of the sheet (important to solder them directly to the Silver and not the copper wire, in order to eliminate the resistance from the solder joint).

I used my Fluke 289 which has 1 uV resolution for the sense-wire measurement (zeroed the reading first, I had an offset of 4 uV), and I then used my Fluke 179 for the current reading.

And the final results:
Calculation:0.001535 V / 9.86 A = 0.0001557 Ohm. =
155.7 uOhm/sq.Compare that to the theoretical
158.7 uOhm/sq., less than a 2 % error with only very crude tools and a quick and dirty soldering job.
