Alcadya, "tinctures" are always done in alcohol. If you do not want to use alcohol, then you can make an "infusion" by macerating the aromatic in sandalwood oil or fractionated coconut oil. I personally prefer sandalwood oil for this process, but FCO has a truly "neutral" odor. However, some concerns with FCO are that over a long period of time, it will change fragrance slightly. However, the same is true of sandalwood (though aging always means a good thing for sandalwood).
What form do you have the ambergris in?