If you are lucky, you'll be able to modify the .ascx page to use some server-side processing to suppress that, or other, link or code.
I would recommend that you give your staff members a role like "staff_admin" and use that.
Follow this link
over to Snapsis.com for some really good ideas. Remember that what you can do in a skin you can also do in an ascx page. I'd do some conditionals to make remove the links for people not hosts or admin. That would include staff_admin.
Remember that any changes like this are changes to the core code. They won't survive upgrades, and you will have to do them after upgrading. And, the ascx may change. So, save code, save notes, etc.