I don't know. I am SUPER paranoid in the "fume" department, but in my paranoid opinion, I haven't found any that are ideal. That having been said, natural is likely be safer (although still potentially dangerous due to the types of oils and spreading agents therein). I just feel like there is so much mixed information on essential oils and, despite their use in medicine for years, it is a fairly recent trend that has led to their widespread resurgence at major retailers.
I hope someone with a lifetime of bird experience answers this, because I am scared to base decisions on anecdotal reports (for instance," __is safe because I use it daily and my 5 year old bird is alive") ...Now if a 90 year old with 3 birds of 80 + years of age said that, it would be a different story lol. GOOD LUCK!