“giddyap” is the spelling from a crossword puzzle I just completed. I had only known it as “giddy-up” from old cowboy movies here in the U.S.A. before today.
Merriam-Webster has “giddap” circa 1897.
Oxford Living Dictionaries has “giddy-up” origin in 1920 (originally US as giddap).
Online Etymology Dictionary has “giddy-up” from 1909, from “giddap” (1867)
Obviously, there is no meeting of the minds re this one. Is there anything more concrete available?