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The wording should be as follows-
In the event of both my wife....as aforesaid THEN I appoint the Partners at my death in the firm of [NAME OF FIRM] of [ADDRESS OF FIRM] as the executors and trustees of this will. However, I want no more than two of the Partners to apply for a grant of probate of this will. The reference to [NAME OF FIRM] includes any firm that has succeeded to, or is carrying on the practice of, [NAME OF FIRM] at my death (including a firm that has been incorporated or formed a limited liability partnership).
It is always best to check with your Solicitors that they would indeed be happy to act as your Executor- just because they have been appointed, does not compel them to act.
I hope this asssits and answers your question.