I know this is the most confusing topic, but the word "hyper" get's thrown around easily.
Most commonly it refers to either specifically the Leaderfins Hyper or in general that type of fin (which I believe is more or less a concept copy of the andronov fin).
By "that type of fin" is usually meant:
-New type of footpocket, heavily angled (but the angle is in the pocket, not in the blade)
-Footpocket is further from the blade than in traditional fins and "torpedo shaped"
-Wings
-Heavy flotation (exception the Leaderfins version that Mullins describes.)
Variants of this type of fin, which are more or less the same concept, but details vary, include:
-Leaderfins Hyper
-"Hyperfins" Hyper
-Gershow fins
-The original andronovs and their many clones
-Waterway glide fin
-The list goes on...
But what they all have in common is a relatively big angle on the footpocket, wings, and specific type of footpocket. The differences are usually in build quality, price, and most significantly blade quality. Unfortunately it is more or less impossible to know what you get before receiving it. Even the exact same fin from the exact same manufacturer may have a completely different blade. They are all individuals. It's a bit of "the wand chooses the wizard" and not the other way around

The reason you see seasoned finswimmers or divers walking around with fins that have been patched or glued in more places than they are intact is not that they are cheap bastards, but because they know that finding a fin as good as they currently possess, is next to impossible.
The "flyer" type of fin, I assure you, is quite different. Mainly the footpocket. The leaderfins flyer (custom) is also very buoyant, but it has a smaller angle in the footpocket and in general a more traditional "flat" footpocket (except it too has been brought back from the blade). The flyer is also a very decent fin and maybe even better for people with very flexible ankles (who don't need the angle so much).
Usually considered ideal for dyn is a floating type of fin, either from the Hyper of the Flyer "family", and for constant weight, usually a non floating one is preferred.
If you don't want 2 fins, I think a hyper type of fin is a relatively good compromise. It is excellent for dynamics, but also very decent for CW (personally I've had no problems at depth, but my depths are hardly WR level). Several WRs have also been made with this type of fin (Natalia).
From custom manufacturers you could ask for some kind of hybrid, like a normal hyper but parts of it made from non-compressible materials, that is almost neutral, etc...
I personally have a sort of a hybrid. A bit less buoyant, the top and inside of the footpocket is soft, incompressible rubber so it doesn't squeeze your feet or get loose with depth. The footpocket is also custom size so that the length is from size 44, but width is from size 46 so it can be fitted with socks and is very comfortable. This is the first fin I've been more or less satisfied with. I'm sure there are betters, but I cannot find any immediate faults in it - unlike any other fin I've ever owned.
But for just getting started, I recommend a any cheap, basic fin. It'll get you going and by the time you are ready to invest more you'll know better what you want.
Now to the actual topic - a friend just told me that he managed to order from hyperfins.ru but it's been over 6 months and still nothing...So, well...Anyone who's tried to get their hands on russian fins knows what I'm talking about. Pretty normal delivery times I guess.