shrug off vs disregard

shrug off is not a noun while disregard is a noun.

Word	Noun	Adjective	Verb	Adverb
shrug off	No	No	Yes	No
disregard	Yes	No	Yes	No

As verbs, disregard is a hypernym of shrug off; that is, disregard is a word with a broader meaning than shrug off:

Other hypernyms of shrug off include brush aside, brush off, discount, dismiss, ignore, push aside.

shrug off (noun)	disregard (noun)
	willful lack of care and attention
	lack of attention and due care

shrug off (verb)	disregard (verb)
minimize the importance of, brush aside	give little or no attention to
	bar from attention or consideration
	refuse to acknowledge