We are TOTALLY doing that! We plan to go get married at the local courthouse the week before and just fly on down and do the ceremony. We plan to say the "traditional" vows in the states and we are writing our own for the DR ceremony. We also will not exchange rings until the DR ceremony.
Honestly, if you think back to weddings you have been to, you never see the bride and groom actually sign the documents with the officiant, that is usually done while the guests are headed to the reception. Nobody will know, or even care enough to ask!
It is pretty easy if you think about it, plus everyone will be so caught up in the beauty and excitement of it all anyway