So I've searched around in both English and Japanese trying to find any information on this specific Tamagotchi. There's a white Morinaga P1 that is considered to be rare. But I haven't found a picture, or mention of this specific one anywhere. I've posted to a English Tamagotchi forum about it, which hasn't turned up anything so far. I've been trying to find a Japanese Tamagotchi forum, but haven't had much luck (I don't read/speak Japanese that well). Part of what's weird about this one is that it came in a box. Looking online most of the Tamagotchi's with brand tie ins came much later, when they switched from coming in boxes to coming in plastic packaging. I guess it's possible that someone found this Tamagotchi loose in excellent condition and never used, and put it in a empty Tamagotchi box from 1996 that they had. Random background info: The Tamagotchi P1's are the first generation or wave of Tamagotchi's from 1996. Morinaga is a Japanese food/drink company, the bird on the Tamagotchi is the mascot for their chocoball line of products.
It's just some stickers that a previous owner has stuck on a normal one I'm afraid, not a special edition. Here's a set of stickers similar:
That does seem to be the case, those are pretty good stickers though! I couldn't tell the difference between the stickers and the shell and I wasn't able to peel any of them off. I wonder if the stickers just felt this way to begin with or if they've hardened with age.