VERY COOL and FUN IDEA!!!
"Dodging" the ever persistent and wonderfully thorough CMs wll be the trick. Unfortunately, I am going to bet that some of the "natural hideaways" likely become home to some trash and other discards from our fellow parkgoers, ordinary trash, gum, other unimaginables, etc. So, beware, brave adventurer!
Some ideas:
In the line to Splash Mountain, as you enter the cave and go down the final ramp towards the ride, there is a sign on the wall on the left which reads "You can't run away from your troubles; ain't no place that far away"...likely enough space behind or to the side to slide in a note
Agree on a seat, last seat of last car, on the MK train and stick it to the bottom
In Exhibition Hall, in the back, there are a handful of cutouts for picture taking (where you stick your head into the cutoff to be the star). It is a lightly travelled area of MK. There are two on the upper stage, pick the one to the left with your back to the stage, hide the note at the base under the cutout leg)
In Belle's Grotto, which is on the right of the castle on the path towards the teacups, there is a small alcove in the wall on the ramp which wraps around and leads up to the stage. I believe there is are some nice small chinks in the wall which would fit a note and be missed by the CMs.
In front of the MK Indy Speedway, there is a formula one car that kids sit in for pictures. You can probably hide a note in the cab or in the struts for the wheels.
In the new Winnie the Pooh kids area across from the Winnie the Pooh ride, there are some nice holes and areas where you could put one, but I cannot be more specific unfortunately.
Switching parks, a very fun place to do what you are thinking about would be the Honey I Shrunk the Kids playground at MGM. The climbing areas and caves of the anthill are full of places where a note might have a chance of surviving a week. One of the best would be if you could figure a way to fix the note inside of the Dog's breathing nose (nostrils) at the top of the climbing area.
In EPCOT, at the end of the Maelstrom in Norway, they make you sit and wait while the theatre empties out, sometimes for 10 minutes or more. There is a white bench there, under a window. Easy to hide a note under the white bench, or perhaps on the windowsill....
In Morrocco, there is a fountain in the back area, where you can probably hide a note (maybe in the fountain if weighted down) or at the base...
This is actually pretty fun...I'll keep thinking and try to come back with more/better options tomorrow...