It might actually be better using 4 separate wires & alligator clips.
With those small Kelvin clips, the 'force' and 'sense' positions are indeterminate by the width of the contacts at the end of the clip. Thus the precise length of the wire you are measuring isn't well defined. With 4 alligator clips, you can position the 'force' lines well outside the sense lines, and therefore the length of conductor you are measuring is defined only by the alligator clips -- if you arrange that only one side of the jaw is contacting, then the position is quite precisely defined.
Not that for resistances of 10 mΩ, you'll need to be careful about offsets and thermal effects.