In this case, no creature type is chosen since Scion of the Ur-Dragon is not entering the battlefield. (Thus, Morophon's last two abilities as gained by Scion of the Ur-Dragon have no effect since no creature type was chosen [C.R. 607.2d, 607.5a].)
A permanent, already on the battlefield, whose characteristics have merely changed (whether by becoming a copy of another object or otherwise) doesn't "reenter the battlefield" this way (C.R. 110.1; for copy effects, compare C.R. 707.4, which covers this scenario, with C.R. 707.5, which covers such cards as Clone). In general, an object enters the battlefield if it formerly wasn't on the battlefield but is now there. See also this thread, this thread, and this thread.
Morophon's choice of creature type is from a static ability creating a replacement effect. The event being modified by that effect is Morophon entering the battlefield. But since The Ur-Dragon which is just becoming a Morophon is not entering the battlefield, the replacement effect from the newly gained ability has nothing to replace. So no, you don't get to choose. Morophon's third and fourth abilities have nothing to reference and thus don't give a cost reduction or bonus to anything.
A permanent, already on the battlefield, whose characteristics have merely changed (whether by becoming a copy of another object or otherwise) doesn't "reenter the battlefield" this way (C.R. 110.1; for copy effects, compare C.R. 707.4, which covers this scenario, with C.R. 707.5, which covers such cards as Clone). In general, an object enters the battlefield if it formerly wasn't on the battlefield but is now there. See also this thread, this thread, and this thread.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)