Want to change university, but concerned about "downgrading" from institute head, and about colleagues learning about my job search
First of all, you need to decide what's best for you long term. If you decide to abdicate and apply elsewhere, then do it and don't look back. 

During this process, you'll want to choose letter writers you trust, and ask them to keep it in strict confidence. You'd do the same for them, no?  People move on, it happens. 

Despite your best efforts, word will always get out...hopefully slowly.  But, see my first point. If you've decided, you've decided, so it's just a matter of time, uncomfortable as it may be.