The correct translation for shapeshifter would be "muodonmuuttaja".
"Muoto" is used for geometrical shapes as well, but it means pretty much all the same things as the English "shape". "Hahmo" on the other hand would mean a character. And if you're wondering why it is "muodonmuuttaja" and not "muodonvaihtaja", there is no particular reason, really. "Vaihtaja" might be a more literal translation from "shifter", but in this context it is just more common to use "muuttaja" (which literally would translate to something like "changer".)
Oh yeah and also "muodon" (not "muoto") is because of the conjugating. So "muodonmuuttaja" would literally be something like "changer of shapes" or "shape's changer".
Hope this was helpful & not too confusing :D