This is to the OP....We are preparing to move our cat from the US, and are using a pet
Moving Company. They strongly advise AGAINST moving any cat via an under-the-seat carrier. One of the reasons they give is that the passenger cabin is generally a busy area with a lot of stimuli that can keep your cat in a hyper-alert state. Given that you are NOT allowed to tranq your cat before travel, this can exacerbate any nervousness.
If your cat is flown in the belly of the plane, it is in a climate controlled area that is (relatively) quiet (or at least there isn't a lot of stimulus) and is generally fairly dark (or mood lit). While you might be nervous not having your cat with you, I'm told that your cat will settle down more easily being in this stimulus-free environment.
The great thing is that you're flying Lufthansa, which my cat will be flying - they apparently have an awesome record for being pet-friendly.
When you arrive at Changi, your cat is whisked off to quarantine - I believe they spend their first evening at the airport, and then are shipped off to the quarantine station.
I hope this info helps - I'm still learning as the process goes on, but this is the website for the agency I'm using - it has some helpful tips that may put some of your concerns to rest:
http://www.petrelocation.com.
Happy trails to you and your cat!!