Those capacitors are there to filter line noise, shunting high freqs to ground.
You should use a safety capacitor ("X2/Y2" rated) since the capacitor is connected probably to the amplifier chassis, or metal parts you could touch. If the capacitor fails shorted, the line voltage can reach the chassis. That's why you see a 1400V capacitor there, to increase safety, but modern safety caps are manufactured to never fail shorted, and can take peaks of several thousand volts.
You can use a plug without ground connection, but instead of cutting the ground plug, in the XXI Century, I'd suggest to add a ground connection to your electrical installation. Electrical safety has improved a lot and installs without a proper ground became illegal in many countries, to save human lifes. You could follow the advice of safety engineers and install a ground connection, even if the laws don't force you to do it, you can save a human life including your own.
Edited: Even if the ground is not connected, the capacitors stay connected across the 220V line, that's why you need an "X2" capacitor there. An X2 safety capacitor is warranted to never start a fire in case of a fail. Also, I see the capacitors are connected before the power switch, that means they will be energized all the time while the unit is plugged to the wall.