I'm pretty sure you will have submit new prints, but it is not that inconvenient. You will be given a list of outlets in your area, to have them done. I don't know if previously holding a permit from another State will speed up the process, since they will start a new background check anyway.
What usually slows things down is if you have moved from another State, since they have to obtain any background info from that State, and some are slower to respond than others. Traffic tickets, should not slow down the process, but if you were arrested, be sure to submit, final disposition documentation.
Good luck, and keep us updated.