If I have your question wrong feel free to elaborate. I think you want to map the type of bicycle to types of uses, each having varying levels of risk. At least, a road bike which encourages fast riding, vs some other bike ridden more slowly.

I don't think that's going to work very well. For one, we simply don't have the data captured regarding what kind of bike was used in accidents. Without data we're only speculating.

That said, there is a another variable: how the bike is used. The fast road bike may be ridden identically to the cruiser, perhaps on a sidewalk at 6 mph. Or someone can take his hybrid on the road, running reds at 20 mph. It is reasonable that the choice of riding has more impact in the chances of the accident that the choice of the particular bike.

Well, I think that you're saying: someone chooses a race bike, it makes him want to ride faster, so he does, and that increases his risk of injury. Then a bike that wouldn't let him ride that fast would be safer. That seems reasonable, but the question is "is it true?" We have no data specifically relating bicycle speed (on the streets) to injury rates. MV speeds yes, but bicycle speeds none that I'm aware of. We do have some data which suggests that higher relative speeds increases the chance of collisions and injury, but a faster bike would reduce relative speeds.

Consider also that if actual use tracks the intended use of bicycles, then that injects other variables. Race bikes are primarily ridden by racers, triathletes, people who ride in groups and train. I can't say that this is completely true, but it seems reasonable doesn't it? These types of individuals are more likely to spend more time training on the bikes, concentrating on specific road skills, and consequently be more skilled than a rider who, not having a race bike does not engage in those activities. So even if we did have the data, it would likely show that the racing bike was safer since skilled riders would have fewer incidents, even if the racing bike itself was less safe.

Finally, in passing let's look at "As speed of that cycle's category, affects the impact of fall." This is actually a bit more complicated than it appears at first look. Strictly speaking, the bike's horizontal speed does not affect the impact of the fall, which is vertical. That's on a perfectly flat, smooth road. In actuality if the road is sloped up then the speed does affect it. If there are bumps or curbs, basically anything you would bang against that's another exception. And of course a rough surface leads to abrasions and potentially rotational injuries, but that's not strictly "impact". And additionally, in my own experience the high speed falls lead to more bouncing and tumbling, more time against the ground and hitting the ground which does hurt more, but the initial force of impact - on flat and level - is similar for low speed and high speed falls. So you may need to re-calibrate your idea with this in mind.