Four square golden pins, twisted 45 degree, soldered on a perfboard, then bent as in the picture, but without touching each other, and with a plastic band to press the DUT against them. Note that the golden pins are pressing against the DUT terminals with one of their edges, and not with their flat side.
The plastic band is a piece of ice cream bucket handle, anchored on the perfboard with two paper staples.
Solder each wire from the Kelvin probe to a pin, and the springiness will do the rest.