I suggest modify the area that the fan is mounted to. You may need to cut the opening for the fan. Use a thin fan guard and rubber grommets to reduce air noise and rattling. Cork can be used instead of rubber grommets. Not all fans are created the same, so replace the fan with low noise versions that can handle tight spaces. I use Panasonic Panaflow fans. Some people may go for the more expensive side and buy fans manufactured by Papst. Though the expensive fans are not always the best because it depends on the computer case and the internal mess, so testing have to be done to use the most efficient and low noise fan.
The fan from Power supplies are not sufficient and should never be counted as a case fan. My power supplies, Seasonic S12-430, uses one 120 mm fan, but it is only controlled by the temperature of the power supply. If the chassis fans go, I would not expect the power supply fan to cool the computer well.