Verb to describe witty use of word or phrase

Solution 1:

quip

As a noun, "quip" means: a witty remark. As a verb, "quip" means: to make a witty remark. (e.g., The author quips with "sternly," referencing both Tom's harsh demeanor and the location Tom was directing to at the back—or stern—of the ship.)

pun

"Pun" isn't just a noun. It's also a verb. So in those examples you gave, you might use the verb "pun." (e.g., The author puns with "sternly," referencing both Tom's harsh demeanor and the location Tom was directing to at the back—or stern—of the ship.)

By the way, since your example comes directly from Tom Swift, I might, if I were you, be inclined to employ a Tom Swifty by adverbifying that eponymous noun for such wordplay. (e.g., Author Edward Stratemeyer Tom-Swiftly quips, referencing with "sternly" both Tom's harsh demeanor and the location Tom was directing to at the back—or stern—of the ship.)

Also, you'll notice my use of present tense in the examples. While the author obviously wrote that in the past, the convention is to use what is called the "literary present tense," always using the present tense when talking or writing about writers or artists as they express themselves in their work, even when that action is complete and in the past.