There is nothing illegal about paying a woman to remain silent about an actual or imaginary episode. It is a legal contract, with consideration passing on both sides.
When this Cohen character talks about these payments being "illegal" or "campaign expenses," he is doing nothing more than proposing a conclusion of law, and it is nothing more than his self-serving legal opinion, having no more weight by virtue of the fact that he was the instrument of payment. The fact that he is behaving so badly at this time gives credence to the suspicion that his entire line of argument has been choreographed by the New York prosecutors with whom he made his deplorable plea bargain.
Those who take the time to read the details of his conduct, both related and unrelated to these episodes, will quickly conclude that he is a low-life scumbag. He grotesquely inflated his charges to the Trump organization, repeatedly lied to his clients, and in most things personified the worst public perceptions of a sleazy lawyer. Even if every word he says publicly is true (excluding self-serving opinion on the law), he is still a scumbag.
And of course, this entire Leftist-Congressional kabuki dance is a sham. It has nothing to do with the Constitutional business of Congress, and the hearings should be shut down immediately.