The word aischune is rendered as shame every time but one in the New Testament, and that one time it is translated as dishonesty.
In Luke 14:9, the man who assumed the highest place was for him is forced to take the lowest place with shame, in humiliation. The crucifixion was a shame that Christ was willing to endure (Heb. 12:2) for the joy that was set before Him.
Paul wrote against the enemies of the cross of Christ, whose end is destruction, whose God is their belly, and whose glory is their shame (Phil. 3:19). The false teachers in Jude are the same — if they were a raging sea, shame would be the foam of it (v. 13).
Paul also says that he, and those who ministered with him, had renounced the “hidden things of dishonesty” (2 Cor. 4:2) This kind of shameful dishonesty would include craftiness and deceitful handling of Scripture.
The true believer is urged to come to Christ, in order that the shame of his nakedness would not appear (Rev. 3:18). Adam and Eve had the impulse to hide when they heard the Lord coming, and this impulse, however irrational, nevertheless makes good sense to us. Nobody wants to be caught out, noboby wants to be revealed, nobody wants to be humiliated before the world in an indefensible nakedness. And that is why the righteousness of Jesus Christ is the only cloak that a sinner should be willing to put on.