All Class D amps I have heard are the opposite of irritating. Go listen and see which ones you find irritating or not. I've heard Bel Canto and Rowland mostly.
Atmasphere has cited certain Pass amps and others I recall that are not prone to irritating harmonics as well. He would know best probably.
I also recently owned a pair of SS Tube Audio Design Hibachi amps that advertised little or no negative feedback and would also fit the bill I would say.
I owned a pair of Carver SS m4.0t amps for many years that performed much like a tube amp. Those were designed to demonstrate a SS amp that sounded identical to a specific tube amp.
I've heard many other musical not irritating SS amps as well. If bad harmonics = irritating then these did not have that affliction either, FWIW.