I think it will complicate things slightly.
Having said that, if you treat the new commissioner as an agent of Parliament.... What I think the Privy Council Office usually does is treat them like a commission of inquiry initially and develop a structure around them. As I said to your colleagues, I think it would be desirable, but I don't think it's necessary.
If the commissioner finds that, after 18 months or two years, it's not working, I would very much hope you would be willing to consider changes.