You need to first figure out what a proper spin rate for the blade you want to use is. I'm suggesting that several thousand RPM may be too high, but that's guesswork -- you need to get a real answer.
Once you know how fast you want the blade to spin, you need to come up with an estimate of the load on that blade. How much force will the grass supply to the blade? How far out from the blade center?
Only after you have those numbers, can you make a determination about the motor power needed, and the gearing needed, to provide the necessary torque at the necessary RPM for success.
This is all very simple math -- basic multiplication and geometry! -- but the problem is in determining the necessary quantities.
For comparison, though, it's hard to find a lawn mower with less than 1.5 HP motor, which is over a kilowatt of power when converted. And even a 3 HP gas engine will get stalled out by wet, dense, grass, although the blade there is significantly wider than 4 inches. As you may know, gas engines tend to have lower torque at lower rpms, and thus end up in a "spiral of doom" once they slow down a bit from their peak efficiency. Electric motors tend to do better on this front.