it is correct for stress to double if displacement doubles for a linear static analysis. if the end displacement of the wrench is 1/10 the length, then i would imagine you need large displacement.
as a check, it would seem that an old fashion hand-crank can be used to easily compute the forces on the tungsten jaws. is this what you are trying to compute? from there you can compute the stresses as a check.
there is often large amounts of noise in contact analysis so the stress peaks are dubious at best. You can look at the contact pressure to get a sense of a sensible value.
On the large displacement analysis: it is a non-linear analysis which will account for the change in stiffness that occurs as displacements exceed the about 1/2 the depth of the member (wrench handle) in the direction of the load. If there are significant angle changes in the analysis and this cuases different leverage to be applied then you will see some differences in results.
Either or both of the above could account for your results.