Yes! Cleats are pretty much the standard in hardwood flooring. Typically, hardwood floors have 'tongue & groove' joints that interlock. First, some definitions of terms that I've used in my answer:
Tongue: the part that sticks out of the hardwood piece is called the 'tongue'.
Groove: the slot it fits into is the 'groove'.
Face: the part of the piece that will eventually be the floor is called the 'face'.
Floor joists: these are horizontal panels that run from one end of the room to the other and rest on beams under them. These provide support and you'll install the flooring on the joists, perpendicular to the direction in which they run.
CLEATS
With cleats, you drive the nail through the tongue onto the floor joists at a 45 degree angle. The cleats (which need to be set in) get hidden by the next piece that overlaps the previous one. The advantage is that all except the last piece in the room will have no nail markings on the surface.
The only con is that you'll need a specialized hardwood floor nailer, that can be pretty expensive to buy ($400-500 for a pneumatic one and $200-300 for a manual one). Needless to say, the pneumatic one is less work (but then again, you'll need to get a compressor for it) than the manual (you'll need a 5lbs mallet to drive a 1.5"-2" cleat in fully). However, these tools are easily available for hire at your local HomeDepot/Lowes (assuming you're in the US).
STAPLES
Now, I've never heard of anyone using staples for hardwood floors. It's more a carpet layer's tool. With staples, you'll also have to nail in through the face, thereby leaving marks all over the floor and ruining the appearance. You can probably use staples to lay down the backer board under the hardwood floor (if you're in a cold weather/windy area, this will help insulate the house by preventing airflow through the slots in the floorboard). Using them on hardwood floors is a terrible idea, and wouldn't recommend it under any circumstances.
If it's a floating floor, your best bet is to take it apart, then put it back together mixing in the new boards so they're not all in one spot.
That said, are you sure the new boards won't match the installed ones? I'm assuming this might be on the edge of a room, so there may not be all that much fading to begin with.
As for using something else, you certainly could, but you'd likely have to go with at least the same manufacturer to ensure the joints match. And I doubt you'd get a better match than the ones you already have in the box anyways.
Best Answer
Hmmm... not sure where you heard this, but as a general rule, the more teeth there are in a saw blade, the finer the cut will be, meaning the edges of the cut will be cleaner, less splintering. So 80 teeth is a "Fine Cut" blade and would be BETTER than a standard crosscut blade, which typically have 40 teeth. But this technically IS actually still a "crosscut" blade. There are really just two types of blades in that regard, crosscut and "ripping" blades. Ripping blades have even FEWER teeth (16-24), because they are meant for hand-held or table saws where you are going to cut ALONG the grain and the higher tooth count would clog up with chips and dust, resulting in burning of the work. Crosscutting is going ACROSS the grain, either perpendicular or at an angle (miter). Within crosscutting blades there are various degrees of fineness in terms of the finish of the cut edges. But with the fineness comes more contact and more heat, so the higher the tooth count, the slower you can cut without burning the wood. The lower count crosscut blades then offer a faster cut, like when doing framing work and the higher tooth counts are for finish work where the looks will matter.
For parquet flooring, you WANT a high tooth count. A step above that are what are called "hollow ground" crosscut blades. They are made of better steel that is machined to be thinner toward the center of the blade so that less of the actual blade makes contact with the wood and deforms the cut edges. Blades with carbide tips will do the same thing because the tips of the teeth, the cutting surfaces, are slightly wider than the blade itself. With each of these improvements in cut quality, the cost goes up so you have to decide where to compromise between cost and performance. If this is a one-shot project, I would opt for the 80-100 tooth standard fine cut blade. But I've also noticed that carbide tipped blades have become so cheap that in many places that is all you can buy, and that's fine, they are good blades.