Isn't it possible that Shukar does have ice powers and just hasn't used them? Point me to the scene where he said "I don't have ice powers."
There are heavy implications that Shukar, and the background Andorians all have ice powers. Note: they all wear thick black gloves at all times, even when in full Starfleet uniform (Prime Shukar being the only Starfleet officer seen with gloves).
Now, some will say that it is merely so the makeup department doesn't have to paint their hands blue (as if they penny-pinched that much). But the real answer is obviously that the Andorians, working with warm-blooded sentients, are protecting them from accidental insta-freezes should they shake their bare hands.
There's also the curious fact that Andorian tonsillectomies require multiple doctors to perform. This is such a dangerous procedure because it must threaten a potential kinetic explosion that will freeze all the medical personnel in the room, if done improperly.
And then, we learn that Stone boasted of killing Andorians (as if), and Psycho was legitimately concerned that Andorians would be guarding a prison camp. Both these characters referenced Andorians by describing them as "cold". They were clearly talking about ice powers, and not some mild personalities or below-average body temperatures.
Discovery has been hitting us over the head with the Andorian ice powers being a serious threat and legitimate concern for all who have dealings with Andorians. Even Emperor Georgiou claims the title of Regina Andor to strike fear in the hearts of her enemies as the supposed conqueror of the Andorians (this is obviously not the case, as she lacks resistance to ice attacks and the MU Andorians are providing healthy numbers to the Resistance).