See Section 2.3.6 Pubslier and Copyright segment. Use ONLY the "With permission of the publisher" statement. Do NOT use the repdouction statement. The reproduction statement is used for eligible materials (not dramatic works, etc) as defined by the law, and transcribed by the authorized entity. Your situation is covered by the first statement, With permission of ...
It is not necessary for the reproduction notice to mention the authorized entity because that is the only entity using this provision. To repeat, in your case, do not use this statement.
In both cases, the number of copies is not relevant and therefore not mentioned. The point is, you have specific permission to create a braille edition of your book from the publisher. That's all you need in order to proceed.