I think OP's cited usage is something of a "malapropism" - it should have been...
hie - Go quickly
I hied down to New Orleans
I hied me to a winehouse
...but as noted in that OxfordDictionaries link, it's archaic.
You could modernize the sample text by replacing hey with full speed ahead, which is still a current nautical usage. But people with a literary background will probably recognize the usage anyway - I still remember it from Olivia's Hie thee, Malvolio. in Shakespeare's Twelfth Night.
EDIT: The full OED contains no relevant definition for hey, but I did find Herman Melville's...
“Hey for London, Wellingborough!” he cried. “Off tomorrow! first train —be there the same night—come!”
...where it seems pretty clear the same Hurry! sense is what's meant. So maybe it's not so much a malapropism as just non-standard orthography.
Thanks to @Spagirl's comment below, I now totally disown all the above! Although I can't find this definition in Chambers online, my paper copy has...
hey for - now for, off we go for
...under their entry for hey interjection expressing joy, irritation or interrogation. That prompted me to search the full OED more carefully, where I find...
1b hey for an utterance of applause or exultant appreciation of some person or thing (cf. hurrah for!), or of some place which one resolves to reach.
I'll leave my earlier text unchanged, since 3 people have upvoted it. But although it might have been a nice idea, I was definitely mistaken.