For this kind of project:
Not only you need to be careful about bleed, but you need to make sure your sticker is a bit bigger than the white area in your book. Otherwise it will look weird and white borders will be visible if the stickers are not perfectly applied! People don't apply stickers perfectly, you need to add a few millimeters to help them a bit.
Because of this, you have some freedom on how you want the sticker shape to be and it doesn't need (and shouldn't) be exactly the same as your white illustration.
Import your illustrations in Illustrator and trace the shapes of your dielines in Illustrator. It will be way more precise.
Printers prefer vector format for this anyway.
I suggest you isolate all your illustrations on their own files and
make sure your illustrator files have the same size as your
illustrations. I personally like to add trim marks to my dieline
files and my artworks; this way I'm certain everything is centered when I import the
dielines and the artworks in InDesign or when I prepare my final
This is how it should look like:
Once you'll have your outlines, you can import the "bleed" one back in Photoshop and use it to create a layer mask if you want.
One "cheat" you can do is to add a white filling on the outside part of the dashed line on my example... and place your illustration under this! This way you won't need to create clipping mask in Photoshop to hide the part of the illustration that isn't the bleed.
Note: You really don't need to add as much bleed as I did. Refer to the url at the end of this answer for bleed info.
The only line you'll provide to your printer is the dieline line, the one shown as a solid line on my example. This line should be in Spot Color (pantone for example) and NOT in CMYK. It should also be "overprint" if you don't provide it on its own file (eg. if you provide the dieline with the artwork in one file)
Printers usually prefer separate files for the print and dieline. Don't forget to also send a JPG proof with both printed illustration and dieline; the printer will be able to see what you expect as result and verify his own work.
Finally, once you'll have your artwork with the bleed AND the dieline, you can prepare your final file with the dieline + the artwork perfectly aligned. You could import all this in InDesign. You can also use Illustrator if you prefer.
This is how your final print-ready files should look like (but with the colored chicken though):
PS: The more corners and sides your dielines will have, the more expensive it will be; it requires more time to create the matrice but also more time to diecut the job. There's more technical issues for the guy who will do the diecut job if your corners are very pointy... it's better to use corners that are a bit rounded instead of perfectly pointy corners.
PPS: It doesn't really matter if your bleed isn't the same exact shape as your diecut. It could even be a rectangle in fact. I'm guessing the stickers will be on their own white sheets and will go in the trash after the stickers will be peeled off from the sheets and applied to the book. Where you need to be precise is with the dieline and the extra margin I suggested you.
Extra info on dielines/diecut, bleed, etc. here