How can I update my HTC Desire when the OTA update is missing?
Yes, it's up to the carrier whether to distribute the update over their network, but it looks like the update did roll out on Orange.  Strange that you didn't get it and can't see it.

That said, updating via HTC Sync is perfectly safe and will not void your warranty.  It's nothing like rooting.

I would think you should be able to take it into an Orange location and they'll update it for you, but I would just do it with HTC Sync myself.  Your link is for the 2.3 update, rather than the 2.2 update; I don't know whether you can go directly from 2.1 to 2.3 with that update, but it shouldn't hurt to try.