Hi,
in such a critical environment, what I would do, is mirror your server and first try the upgrade on your copy.
Once it's up and running and figured out all the glitches... you could do it on your live server.
This kind of big upgrade is probably going to give issues. But on the other hand... not upgrading it will also make you run into issues sooner rather than later, especially when PHP 5 will go stale...