It's basically impossible to even discuss this question without sizeable spoilers, so if you're sensitive to that sort of thing, turn back now. You've been warned.
In an interview with Entertainment Weekly, showrunner Marco Ramirez unequivocally stated that the dragon under New York was not Shou-Lao:
That dragon skeleton — that wasn't Shou-Lao the Undying's, is it? It's just a pile of bones implying that there had been dragons all over the world and one wound up buried under New York?
Yeah, it's the second one.
Knowing that, we have to presume that Danny is using the word "desecrate" in a less literal sense. Without more information about K'un-Lun and Shou-Lao (which we don't currently have), it's hard to be totally certain of the intended meaning, but it's likely that he meant it in the sense of "to treat disrespectfully"; the other definition doesn't seem to make sense, for the reasons laid out in the question. And really, "disrespectful" is the least you could say about ingesting the remains of one of Shou-Lao's relatives.
The use of "desecrate" is a little bit odd, but it's not much stranger than anything else Danny says, and does seem to communicate just how reprehensible he finds their actions.