The earliest instance of "word of hand" that a Google Books search finds is from Maurice Powell: An Historical Welsh Tale of England's Troubles, volume 2 (1821):
"... Oh! and give me fair play, and I'd soon see the backs of the whole generation to tarn us out, your honours, the bogtrotters ! and Mr. Morgan was aslape on the binch, and so one of them knocked him down—bad luck to him—and, oh, how I'd like, now they're all here, just to rapate to your honours, by word of hand, all de rist of the business," and, looking toward the puritans, he grasped a short stick that he held in his hand.
It's difficult to say whether the point of the speaker's use of the phrase "word of hand" is to convey the meaning "in writing" or the meaning "by physical violence"—or whether it is just a burlesque playing on the confusion of the character's drunken state and his Irishness.
The next Google Books match appears to have a narrower meaning. From Alexander Slidell-Mackenzie, Spain Revisited, volume 1 (1836):
The political conversation was again renewed, and the sententious young muleteer managed, while he sustained his argument, to carry on by word of hand, wholly unobserved, as he thought, a little practical gallantry with the willing damsel behind him.
Here it appears that "to carry on by word of hand" means "to communicate by touching."
Subsequent instances tend to follow the sense of “in writing.” From a 1912 U.S. Senate inquiry into the sinking of the Titanic, we have this dialogue between Senator William Smith of Michigan and Second Officer Charles Lightoller of the Titanic:
Senator SMITH. Who would give the command [to reduce the ship’s speed]?
Mr. LIGHTOLLER. The commander would send orders down to the chief engineer to reduce her by so many revolutions.
Senator SMITH. Through a megaphone?
Mr. LIGHTOLLER. No, sir; by word of hand.
Senator SMITH. By speaking tube?
Mr. LIGHTOLLER. No; by word of hand; notes.
Senator Smith’s failure to correctly interpret “word of hand” suggests that he was unfamiliar with the phrase, which in turn suggests that “word of hand” was not a widely used in the United States. On the other hand, William Thomson, a New York doctor, writes in Brain and Personality, eighth edition (1908):
The second kind of speech consists of words which go from us , or which we ourselves utter. This division of the faculty of speech is wholly different from the first, because in that we are passive and receive the words, while in this we are active and ourselves give forth the words. We do this either by word of mouth or by word of hand in writing, and to thus express ourselves an entirely distinct mechanism is required, because it involves muscular movements.
But we do still see examples that explicitly distinguish “word of hand” from “writing.” For example, from Porter Browne, “Stranger Than Fiction,” in The Circle magazine (February 1908):
The fair maid and you mutually agree that to speak plainly, papa is impossible. You decide to elope, carefully selecting as plotting place a quiet nook where there are foregathered only about seventy-five or eighty of papa's friends and retainers, and then, lo! all at once the fair maid disappears, leaving no footprint, nor word of hand or mouth or fountain pen.
In this case, the meaning that the author has in mind for “word of hand” is not at all clear.
Another sense that “word of hand” can have is words tied to hand signals—not sign language per se, but verbal language referring to hand signals. From David Katz, The Vibratory Sense and Other Lectures” (1927) [combined snippets]:
Our ten fingers are the simplest and most natural counting-machine ever possessed by man ; many a numerical term is covered by the word of hand. In the language of the coast-dwellers of the Gazelle-Peninsula, "lima" means hand, i.e. "five", a “utal a lima” (a triplet of hands) means “fifteen”. Among many nations two hands or a “half man” means “ten”; a “whole man” means "twenty" (the sum of the fingers and toes). Likewise, the history of counting on the fingers, a habit still met with in every A-B-C- infant, can be traced back to the dim past of the human race.
And in some situations “word of hand” may refer specifically to sign language. From Communication & Cognition, volume 11 (1978) [quotation not visible in snippet box]:
Before the possibilities of video-taping, the language and literature of the deaf were part of an "oral" tradition passed from generation to generation by "word of hand" in the collocations and stories of American Sign Language.
Finally, “word of hand” has been adopted in marketing as way to describe logo-branded pens as promotional devices. For example, from Promotional Pens, an Australian website:
Word of Hand Marketing
Word of mouth is a stellar advertising strategy, but with a constant barrage of information, it is not always likely Sally will remember which plumber Suzie recommended. If Suzie has an extra pen laying around with the company logo and phone number on it, however, word of mouth advertising becomes work of hand marketing. A pen can change hands many times before the ink runs dry, so providing customers with a few business pens can result in exposure to dozens of people.
I suspect that work in the body copy of this blurb is a typo for word.
In most instances, “word of hand” is an unconventional way of saying “written word”—generally as a contrast to the familiar notion of “word of mouth.” But it is not an especially common expression in any event, and in particular instances it may refer to something else—for example, communication by physical contact, words defined in terms of hands or hand signals, sign language, or advertising with branded tchotchkes. Unless the author or speaker explicitly identifies the intended sense of the term, you’ll have to look for contextual clues to determine that sense.