If I'm trying to trade-in a vehicle that's been paid off for a year and that my late grandfather co-signed with me, will I be able to trade it in without a lot of hassle?

Is the title in your name and clear of any liens?  If not, this is going to be a hassle.  You will have to get the lender to release the lien.  If the title is in both names, you will need something from the estate transferring title into your name alone, probably an order from the probate court.