There’s very clearly a correct thing here, it’s just that—for four decades—Bruce Springsteen himself had it wrong.
It’s apparently been a thing for some time now that Springsteen fans will argue over which word is right, since one can clearly be heard in the song but the other is printed on Springsteen’s website and in his official songbook.
That comes straight from Springsteen’s longtime friend and manager Jon Landau, who said it’s “sways†and that “any typos in official Bruce material will be corrected.†He also added that dresses “do not know how to ‘wave.â€â€ More mysteries should be solved by just asking the people involved.