I've been reading about the imminent hard fork between BTC and the new Segwit2X (B2X).   My question is, if I have 1BTC in my wallet before the hard fork, then after the hard fork I will have 1BTC + 1B2X.  However, using a wallet such as Exodus (software) or Ledger (hardware), how would I access the forked coins?  Do I have to wait until the developers release updates that recognize the new forked coins?

Am I looking at this wrong?  I've heard that the safest way to ensure you retain your funds during a fork is keep control of your own private keys (which I do).  But, has anyone experienced a prior hard fork, and how do you "access" the new forked coins using their private keys?

Thanks guy