Is a 2W resistor sufficient to dissipate 0.6W of power?
Yes, the 2W will be cooler, because it's bigger, so has a larger thermal exchange surface with air.
If you don't have a 2W 240 ohm resistor in stock you can use four 1kOhm 0.25W resistors in parallel. If you put them in the airflow of the fan they should stay well below finger-burning  temperature.