That will work fine as is. There is no Ardunio in circuit, so none of the 5 volt, 40ma, 200ma limits apply. Assuming about 20ma draw for the LEDs, that is about 100ma total for the 9 volt battery, and the sum of the LED voltage drops should be enough less than 9 volts to pick a good resistor value. Unless using LEDs with a color that has a higher voltage drop. Orange and Blue would not work.
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