If it's in the 47 MHz range like most cheap R/C stuff is,
pretty much anything attached to it will recieve [sic] a
signal sufficient to make it work. Sure, length will make
a difference in how well it works, but you may be able
to get close enough by guessing.

And inasmuch as the OP has the original antenna, there's no guessing about
the "correct" length.

In short, you don't need the "original" antenna.