Setting Edit Permission at the record level.

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SharePoint

Posted this incorrectly, reposting.
I am needing a way to have the creator of a list item to designate an individual in the record (list Item) to have permission to edit their individual list item without compromising the list's permissions to restrict people to see only there own items.

I have a list called Requests, the creator of a request is not always the "Deliver to" in the request and sets this to someone in the item. I need the "Deliver to" to close the request instead of going back to the created by and asking them to close it after the delivery is made (an external process).

Can this be done, through a workflow, java script, or another method? Can you suggest any good books/Sites on Site and List permissions in SP? I have to deal with unique security permissions that are conditional so I need to become an expert with permissions.

Thanks for any help you can provide.

Mike