According to Google Ngram, men are shrugging their broad, heavy, great shoulders less and less.
But before that, let's see what men and women shrug most often according to Google Books.
For men I entered the expression shrugged his *. The asterisk symbol which follows will display the first word that comes after the pronoun his. Note that it is superfluous and counterproductive to search for "he shrugged his" because the possessive pronoun already tells us the subject is male and moreover you would ignore the innumerable instances where a proper noun or noun phrase would be used, for example "Daniel shrugged his", "Her husband shrugged his" etc.
For women I repeated the same operation
Interestingly, people tend to shrug off females i.e. shrugged her off. I went back to my first Ngram and repeated the experiment with shrugged him * The following results were: shrugged him off, shrugged him away, shrugged him aside
For the feminine Ngram chart I wondered if a woman might shrug her pretty hips, finger, eyes or eyebrows. I entered the terms: shrugged her shoulders, shrugged her pretty *, shrugged her thin *, shrugged her plump *, shrugged her white *
The results proved conclusively that shoulders is the only part of the human body associated with the verb, shrug.
In the following "masculine" Google Ngram Viewer I added the terms: shrugged his heavy *, shrugged his great *, shrugged his thin *, he shrugged his broad *, he shrugged his shoulders, and shrugged his shoulder. Once again the asterisk substitutes the first word that follows
Men only shrug their great or massive shoulders, I was hoping for something a little more titillating. You may have noticed that I forgot to add he shrugged his massive * but if you don't believe men have massive shoulders, do the operation yourselves...
Oh, all right. I'll do it myself
Unsurprisingly, the adjective broad is most commonly associated with male shoulders, but what I do find peculiar is the drop in the number of times men shrug their shoulders (see the penultimate chart), apparently there was an impressive peak in the 1930s followed by a steady decline. I wonder why?
Is there anything else that can be shrugged, besides shoulders?
Yes! You can also shrug these things off
I Googled "shrugged off the" in Google Books and found...
shrugged off the news, leaflets, meaning of, notion, denial,
sand, role, injury, idea, arm, past, loss, signals,
irritation, annoying sth, blazer, Nazi's, thought, problems, crazy
things, worry, traps, overcoat, indifference, eerie sensation,
backpack, criticism, belt, ugly memory, prospect, nervousness, crash,
police assault, comments, comparisons, feelings of guilt, yoke,
gratitude, efforts, question, bad news, phenomenon, complaints,
fraternal hand, encounter, feeling of impending doom, report, deal, treason accusation, feeling in disbelief, dream, coat, lifelong
sacrifice, offending limb, snide remark, London damp, incident,
possibility, knapsack, man's hands, fact, cool chill, shawl,
gloomy mood, frontier town mentality, pain, daily calls, feeling of
apprehension, suggestion, analysis, prudish atmosphere, stories,
feeling of being watched, threat, blouse, burden, suit jacket, apathy,
pack, horrendous accident, wealth and power, results, girl's embrace,
punishment, consequences, hood of the anorak, cold, self-pity, first
signs of, advice, doubters and the snipers, slight, pressure,
hands that attempted to grab him, accoutrements of their past, stigma, snub, environmental costs, cares of the world, attacks,
charge, tendency, first frost, abuse, compliment, request, hurt,
negativity, blankets, effects of the weed, wasted emotion, guy's
hand, darkness, failure; Chinese, the Mongols, and Siamese; mantle
of religion, thefts, warnings, whole business, economic and social
problems, letter, old man, reprimand, critique, shackles of
traditional morality, lack of popularity, blows, conflict, cape,
announcement, yellow jacket, duty, camisole of Marxism, tremor of
excitement, sleaziness swirling about him, stick as he had shrugged
off the carrot.; deepening suspicion, happy memory of that episode,
I stopped at page forty, but as you can see there are many other things besides shoulders which can be shrugged off, and one of them being hands.