Hi and welcome to the forums.
You can do what @Wellenreiter has described.
basically your Feathercoin data directory by default should be in C:\Users\YOURUSERNAME\AppData\Roaming\Feathercoin
In that folder you’ll find your wallet.dat as well as your downloaded copy of the blockchain.
When you uninstall feathercoin-qt from “add and remove programs” it removes it from C:\Program Files\Feathercoin but it leaves the stuff in your AppData folder alone
BUT!!! Always be on the safe side - Make a backup of your wallet.dat and your private keys separately…
Then uninstall Feathercoin 0.9.6.2 and just simply download and run the installer for 0.16 .
The 0.16 installer should find your Feathercoin data directory and work as normal. You might have to wait for it to rescan the blockchain but this is pretty quick on most computers…