Non-dairy non-chemical subs for heavy and sour cream

If you store some cans of coconut milk (full fat) in the refridgerator the fat of the milk will rise to the top you can scoop it off. This works so well that you can even make whipped cream out of it. Also for sour cream, you could try some shaken up full fat coconut milk with lemon juice or vinegar, possibly soy, almond, or rice milk with lemon or vinegar may work as well!

Flexi creme can be used as a substitute for heavy cream . http://www.flexicreme.com/

Plain non-dairy yogurt works for sour cream, for something like a coffee cake you can add a teaspoon or two of lemon to room temperature soy milk (or other non-dairy "milk" product) and let it sit until it starts to curdle and use that (in the way you might sub buttermilk for sour cream or yogurt in a baking recipe).
For heavy cream I often use the thick cream at the top of a can of coconut milk.

for sour cream, I'd use greek yogurt. Heavy cream may be more difficult to sub.

There is a product called MimicCreme, packaged in an aseptic quart, made from nuts. It appears to have been formulated for food service use, and is meant to mimic cream -- it's pretty heavy!

There are lots of non chemical options, but it really depends on how the heavy cream is used in the recipe. There is a non-hydrogeneated toffuti sour cream that works decently as a sour cream, but it needs a bit of tinkering. I have a lot of recipes on my site (www.couldntbeparve.com) that use healthy substitutes in recipes that commonly use cream like ice cream and panna cotta. If you have a specific recipe that you want to convert to non-dairy feel free to send it to me and I will help think of creative ways to do it.