little, slight, small | careless, indifferent | nonchalant | dismissive | helpless, hopeless, resigned | tired, weary | apologetic | self-deprecating | expressive | mental
With a mental shrug, he decided to tell the truth.

Gallic

give
The boy gave a slight shrug and walked away.

in a ~
She lifted her shoulders in a little shrug

with a ~
‘I don''t know,’ she said with a shrug.

~ of
a shrug of resignation

a shrug of the shoulders

lightly, slightly | carelessly, dismissively, indifferently, negligently, nonchalantly
She shrugged nonchalantly and turned away.

impatiently, irritably | apologetically | helplessly, ruefully
He shrugged helplessly and said nothing.

expressively | just, merely, only, simply
He merely shrugged his shoulders in reply.

PHRASAL VERBS shrug sth off

be able to, can/could, try to
The team have been able to shrug off their recent failures and perform well.

try to