My aunt deeded a timeshare she purchased to me, my sister, and my brother. I have been stuck with the fees and would like to know if a quitclaim deed could be used to unload the timeshare. Would a grantee signature be needed in VA?

Probably not. But you are thinking about conveying it to some person selected randomly from the phone book? You do know that such person would probably not pay the fees, and they could still come after you>

Is the timeshare fully paid for? Unless you can find someone willing to accept the timeshare, the company will come after you for payment. Since the ownership is split 3 ways, you can sue your siblings for their share of the fees.