E-mailing

This is a good idea as an end result, but the wishlist module is not the appropriate place to create this functionality.

Organic groups strikes me as one way to manage subscriptions for wishlists. Use the simple og homepage that ships with the og module, make your wishlists one of the data types that must be associated to a group, then have your users register within groups. Within a group there are options to subscribe, maintain subscriptions and such. I've not tried this configuration, but I do know that OG does a great job at handling subscriptions and notification of new content, which is what you are looking for here.

You might also try looking at actions.module or workflow.module. I'm not as familiar with them, but one may also meet your needs. There are many email management modules on the contributions page and you may find another one that you can combine with wishlist to get the result you want. The wishlist module creates nodes to allow it to interact with other modules in the system.