In the original, if either the stock transfer books of the Company _or_ the book entry system of the warrant agent are closed, the person becomes a holder on the next date when either are open.

In your rewrite, if both the stock transfer books and the book entry system of the warrant agent are closed, the person becomes a holder on the next day when both are open.

If you search for the language of the original, you'll find a bunch of examples of the exact same language. I'm with the others that this is well-litigated language that no one wants to change. https://www.bing.com/search?pglt=161&q=Each+person+in+whose+....