To clarify what I mean about looking sloppy: I once read a short story that was a sci fi riff on the Biblical story of Abraham nearly sacrificing his son. The characters go back in time, in a time machine, encounter Abraham, and he thinks they're God. One of them tells him to sacrifice his son. Another stops the sacrifice when it's about to start.Depends on whether you're retelling the myths or riffing on them.
If your book includes a straight retelling of the Minotaur story where Theseus gets eaten by the Minotaur and it's Daedalus, not Icarus, who falls in the sea and drowns, that will annoy the reader. At least, it would annoy me. But if it's a riff, clearly not a verbatim retelling, it's okay to fracture it. You could, say, have Icarus narrate the story and say, "You might have heard how me and my dad escaped from the Minotaur on wax wings and I flew too close to the sun. That's not really how it happened, here's the real story...."
Basically, if you're changing the myths, you have to make it clear that you know the original story and your change is deliberate. Otherwise, you just look sloppy.