Mixing = a few swirls of the hairdye brush (something you'll be doing in the bowl anyway to get the edges and pick up product). Looks like Wella, Garnier, L'Oreal and Clairol all have formulations without ammonia and most hairdyes marketed as "natural" have no parabens too. Though, be honest with yourself - hairdye is chemical and you are putting it on your head. The swapped ingredient for ammonia still has to do the same thing or the product doesn't work.
I personally moved on to henna nearly 10 years ago. That's about as natural of a hairdye as you can get, and yet I still question if its a great idea leaving it on for long exposure (you leave it on for way longer than "normal" dye) because I can tell I'm absorbing some through my system and making my liver work harder (for a vague TMI). But, I use henna because it looks better than chemical reds (fading has to do with size of dye molecule vs lawsone ~permanent keratin bond =color doesn't fade, and looks more natural), not because I'm overly concerned about "chemicals". If I were, I couldn't justify using body lotion.
Good luck.