Hypocrite is a Greek word that is just spelled a little differently than it is in English (hypokritai). However, we give the English word a nuance that isn’t implied in Greek.
The first part of the Greek word, hypo, means under, and the second part, kritai, means judge (it’s where we get the English words critical and criticize). So in the Bible, a hypocrite is a ‘lesser judge,’ or ‘little judge.’ In other words, they are not a proper judges in a courtroom; no, they are just little judges who are very judgmental of the actions or conduct of others in their day-to-day lives. So the meaning of the Greek word is basically, ‘a judgmental person.’
This differs from the meaning in English: someone who doesn’t follow his own advice. Does this mean that ‘hypocrite’ is the wrong word to use? Would it be a mistranslation? No.
Jesus likely said all these words in Aramaic. According to the Aramaic texts of the Gospels, he may have originally said something very close to the modern English meaning. It appears as a two-word phrase (nasb'ay b'ahp'eah), which we could translate as face taker. This describes pretenders, or those who put on a false front. Therefore what was likely the original Aramaic phrasing said by Jesus carried the same meaning as the our modern word hypocrite.