Both words are illiteracies. The prefixes ir- and dis- are superfluous. Say regardless, unmindful, heedless, anyway, or even the wordy in spite of everything and thus avoid a double negative (dis- and ir- plus -less): "Regardless (not disregardless or irregardless) of what you say, I shall do as I wish."
Dictionary of problem words and expressions. Harry Shaw. 1975.