How would you handle this?

Tiger One is absolutely right. It is possible that someone on the old staff wanted the job too and that can create a problem. You are better off interviewing the old staff and be straight forward with them. Tell them exactly what you are going to do and see how they react. If your offense is based on the pass and the coaches have been running the veer, they might not adjust. It is like hitting your head against the wall if they aren't in your corner. You got the job because you where the best candidate, put together your own staff, loyalty is the key.