Here's an answer from somebody who actually knows what he is talking about.

I am a Muslim who is happily married to a Chinese (ex-buddhist) lady. When my father in law passed away recently, I allowed my wife to follow whatever rituals that I believe are not against the teaching of Islam. As for the chanting, (the one where the eldest holds this branch) I even participated in the ritual as an observer, as a sign of respect towards my father in law. But of course when the monk gets the congegration to bow towards the buddha, of course i got my wife and myself not to bow along because only Allah is worthy of my bow.

When the ritual to send the body to the crematorium was happening, I still participated in the ritual including kneeling as a sign of respect, but I stopped short of bowing to my father in law.

My advice to you is, you could respectfully get a brother to replace you in the ritual, and only participate as an observer, as a sign of respect. There is no problem in that as long as you keep your faith true, and bow to no one else but Allah. If you want to talk about this more, shoot me a PM. I'll be glad to answer any other questions that you might have...

according to my wife, holding joss sticks has nothing to do with buddhism... it's more of a cultural thing for the chinese people...