Solution 1:

As a person guilty of saying "under", I personally agree that "below" is more appropriate, as it refers to two-dimensional layout (top-view of the keyboard), while "under" is typically used for three-dimensional things in which one obscures the other.

That being said, simply calling it a "palmrest" would've done a much better job.

Solution 2:

I think it is entirely a matter of perspective. In terms of using below or under, you can use either if you decide your hand is under the keyboard.

As Jane Mairs (The editor of Merriam-Webster's learner's dictionary) explains:-

"Under can have the same meaning as below, as in these examples:

We sat under a tree and rested. (Or, We sat below a tree and rested.) Draw a line under each word you don't know. (Or, Draw a line below each word you don't know.)"

In the context of the question this is the same sense, so I would say both under and below are equally applicable. However...

As I said I really think this is a matter of perspective. Is your hand really 'under' the keyboard? Well I don't think so. I would say your hand is 'adjacent' to the keyboard.

Of course if the base of the laptop is at any kind of incline then your hand could well be marginally under the keyboard.

In my view your hand is adjacent to the keyboard unless the keyboard is being held in the air with the front of it pointing at the floor.

But for all intents and purposes in everday vernacular I'd say under or below, the choice is yours!