Try it like this:
1. Probe near the end of the cable, to avoid transmission line effects (the frequency is still relatively low so this should be okay)
2. Join grounds, from the cable connector to the probe connector. Minimal lead length preferred, maybe can just hold the two together with the connectors touching.
This should minimize common mode interference, without needing a ground plane and filtering setup. Note that ferrite beads on the probe, or generator output, won't have much effect as the impedance is quite high (100s to k ohms). With a short between them, the impedance is low, and at least a significant effect should be seen if it is due to CM, and further improvement may be seen with adding ferrites.
Common mode coupling would most likely originate from the generator, from having a poorly wired/grounded connector or internal paths that end up as conducted emissions.
Also, a good probe should be fairly immune to common mode (electric fields) in the orientation shown, but who knows.
Tim