You're right to distrust the hinge. Many people have cracked their screens by inadvertently opening the cover from the wrong side.
There are a number of covers out there that don't employ the Kindle's hinge system to securely fashion the Kindle in place. I believe some of those options are in the Kindle store, but I could be wrong about that. My favorite covers for the Kindle (not on the Kindle site or affiliated with Amazon) are the
Oberon covers. You can get them with straps or Velcro backing. I've recommended them so many times now that I'm afraid people are going to start thinking I'm getting a kickback from the company. Other folks here can tell you of other covers, some of which may met your personal needs better (for example, there's
AquaPac, a company that produces waterproof covers, and another company whose covers are built like a virtual tank for maximum protection).