From what I've read, corroded batteries are a possibility but not likelihood. Additionally, it seems that corrosion can be chipped off and thus it is possible to make corroded contacts usable.
As for the screwdriver, my practical Father proved to me that the screws of vintage tamas are not special when he unscrewed them easily with our set of small Stanley screwdrivers (I think Stanley might be some Canadian brand, and not necessarily special). The screws he took out were from an English P2 and English Angelgotchi, which I'm assuming are the same as the Japanese ones since I've never read anyone mentioning the screws were different between localizations. Additionally, he summed it up that it would be impractical to use special screws for a toy like that as it would be too much of a hassle.
One thing I should mention is that my father has likely perfected his technique for taking out screws since he remarked, when I asked him to take my Angelgotchi's screws out again, that I may not be used to doing it. Another thing, save the tab from your Angelgotchi since I've heard of many people putting it back in to save battery power. It shouldn't do any harm if it is used with new batteries, although I hear storing tamas long term with batteries in them is not recommended.