Heavy cream is cream that has 35% milk fat, with the rest of it being as close as makes no difference, water. Assuming you use 1 oz (28g) of cream in your coffee, then you've just ingested approximately 10g of fat, for an energy intake of 90 kCal.
If you look at food labeling in the US, you will see that all labels specify the % daily value that a particular serving of the food in question contains. This is all based on an assumed daily caloric requirement of 2000 kCal. With this framework, your caloric intake from 1 oz. of cream is 4.5%. This is not a lot.
So, to restate your question: "What is the impact of ingesting 90 kCal, or 4.5% of your daily caloric requirements, of fat on the hormonal responses of the human body to fasting?"
I would expect the effect to be negligible. In absolute terms, just based on caloric content alone, that is a trivial amount of energy that you have ingested.
But just for the sake of argument, let's assume that this amount of energy intake were enough to reverse the hormonal context evoked by fasting, that is, the metabolism would be switched from fasting state to feeding state. Now, imagine back in pre-history, a hapless hunter that hasn't eaten for a day or so, due to some bad luck. His body is actively releasing FFAs from adipose tissues and oxidizing them for energy, everything is humming along nicely. Then, incidentally while tracking some prey, he comes upon some wild berries, enough for roughly a handful of food, and eats them, only to collapse a little while later because this trivial amount of nutrient intake was enough to transition his metabolism from a state where it was relying on internal resources for energy to reliance on external energy resources which never materialized. I think this kind of metabolism, while theoretically possible, would be evolutionarily eliminated pretty quickly.
I also expect the effect to be negligible due to the nature of the food that you've eaten, specifically, fat. In order for a "meal" of pure fat to effect a change in your metabolic context, that would imply that somehow, your tissues were able to detect exogenous FFAs from your meal, and differentiate them from endogenous FFAs from your adipose tissue. So far, nobody has proposed a mechanism by which this would happen. We know that fat does not evoke an insulin response, so, at the very least, your pancreas is "blind" to ingested fat. Most likely, all tissues treat all fats as fungible, irrespective of their source. At a cellular level, any FFA molecule is just as good as any other for mitochondrial oxidation.
With the above in mind, I can answer your question like this: "The most likely outcome of ingesting 1 oz. of cream is that 1/3 oz. of adipose fat that would have otherwise been oxidized for energy will now be spared due to the ingestion of 1/3 oz. of FFAs from a cup of coffee."
Personally, I consider worrying about 1/3 oz. of adipose tissue obsessive. But, maybe you're a purist, in which case, by all means cut out the HWC.