is it possible that hyponatremia causes hand swelling?
yes

is it likely that hyponatremia causes hand swelling?
no. even the Dr in Lynn's article says 9 times out of 10 it is just blood/fluid pooling in the extremity ,whether upper or lower.

That is why many of us notice hand swelling after just a one hour walk or hike so it cannot be hyponatremia that quickly. The Dr in the article is referring to Ironman-type stuff where severe hyponatremia would cause much more than some minor hand swelling, ie, brain swelling with loss of coordination, even seizures, etc, etc. Also, he is on the Gatorade payroll. I am not. There is an appropriate use for electrolyte replacement but a one hour walk is not one of them. Even a full ride up and down Whitney should not pose a problem unless it is 90+ degrees, the person ill with bad vomiting or diarrhea, certain chronic illness, extremes of age, certain medicines, other exceptional circumstances.

People often carry a baton or a stick around to squeeze intermittently (instead of statically/isometrically) to pump the veins out, so to speak. That does help.