That is correct. What you need to know is your password that keeps the private keys safe. Sometimes people mix that up.
Most of the time, people saying that you must know your private keys actually mean that you must control your private keys. Web generally wallets manage your keys for you so you don't have access to them, and anyone with direct access to the keys is capable of spending the coins. If you're using Bitcoin Core, all of your keys are in your wallet.dat file, so as long as you secure it in some way (such as the built-in encryption) you should do fine. No one that I've heard of has memorized a private key, though similar (and potentially less secure, if done wrong) effects can be achieved through the use of brainwallets and wallets with memorizable deterministic seeds.
As for your original question, just back up your wallet and install the new version as everyone else has said. It's as simple as that.