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The safest thing is to use the correct cables. You might find just connecting the 4 pin works and it might work fine, however that means the pins are carrying more current and so are the copper tracks. The reason they have 8 pins is because at maximum power draw, you need the extra wires and pins to spread out the current drawn to prevent overheating and burning out the connection and the copper tracks.
You really would be safer getting a new power supply to be honest. The motherboard might not even boot without all 8 pins connected. Usually if it is acceptable to use just a 4 pin plug there would be a cap over the other 4 pins or a note in the manual.
You can get adapters that convert 4 pins to 8 pin, the problem here is you still end up with too much current going through the 4 pins and 4 wires.