As you have already covered off lubrication, the only real issue is cleaning, and most of this comes down to keeping the interior dry, and wiping down the exterior.
From Eagle Music:
After each use, clean out the bore of your whistle and remove any moisture or dirt that has settled there. This can be done with what is called a flute/whistle mop which is made from lint free wadding held in position by thin wire that is wrapped around it and also forms a shaft and handle.
Wiping down the mouthpiece with a baby wipe and then drying it after every use is also recommended.