I'm using Kleopatra (actually gpg4win) on Windows. I've created PGP
Private keys, and I would like to store them on my usb stick (e.g. be
able to encrypt files only if the private key is available - that is,
if the usb stick is in the drive).
You actually don't ENcrypt files with your private keys. Normally, public-keys do the ENcryption, private keys do the DEcrpytion or signing.
You don't get advantages from carrying your private keys with you. When windows and Cleopatra are set up properly, the keyring-files are protected by passwords. For example when using SMIME on Windows-mashines, the Keys are encrypted with your windows-password.
If someone is able to extract your private keys from your computer, he would probably also be able to install a keylogger on this PC and copy your keyrings from your USB-drive at the moment when you attach it to that PC. Anyone could write a .com that searches for .pgp-files and copies them to a specific location, when a removeable drive is mounted (via autostart-routines).
I agree that it is absolutely reasonable to backup your Keyrings from time to time and store them away, but as soon as someone steals your PGP-keyrings, you have gained nothing. What kind of USB-drives would you use? Corsair Padlocks?