I got the answer from another source (meaning I figured it out myself). For anyone who needs to know, the answer is no: do not cut any wires. Leave the capacitor wires/circuit alone.
The key is to remember that the only difference between 120v and 240v is that 120v is wired in parallel, while 240v is wired in series. If you were to follow the wire diagram on the motor cover without thinking about that fact, you would leave the blue wire disconnected, and jumper both incoming hot wires from the power cord. This will quickly burn out the motor -- possibly literally, starting a fire.
The diagram in the owner's manual is not much better.
Instead, do the following: Connect the black and brown wires FROM THE MOTOR to each other -- do NOT connect the black wire from the power cord to this bundle. This puts the internal connections to the motor coils in series, which makes a 240v circuit work. Now, to connect the actual power lines, connect the white wire from the motor to the white wire from the power chord. Connect the blue wire from the motor to the only remaining power line, which will be the other black wire (from the power cord).
In a 220v circuit, it does not matter which side of the power lines goes to which side of the motor. Both are "hot". I put white to white just to keep it simple and easy to remember. You could reverse the connections and it would have no effect. But again, keep it simple for the sake of clarity -- white to white, blue to black when connecting the power leads to the motor coil leads. The remaining leads, one black and one brown, are both internal motor connections. They connect (jumper) to each other, not to the incoming power leads.
The green wire goes to ground. It is already connected. Leave it alone.
The red wires go to the run capacitor. Leave them alone.
If your wires have different colors, you can use a multi-meter to check for continuity to see which wires go where -- if you keep in mind how a set of motor coils in series are meant to be wired.
If this does not make sense, hire an electrician to do it right. Don't play with high voltage if you don't understand what you are doing.
Good luck, and be safe!