What is it you would want to write then?
Do you have an actual offer or confirmation you have the job?
If you do, I'd wait. Aside from the fact that I'm not quite sure what it is you would want to write, they were clear that and why they need time to get final approval and "hassling" them after only a week in some way or another (even if you don't see it as hassling) won't be received well.
If you do not have an offer and some kind of feedback is still pending, you can and should follow up in an e-mail or call.