Would this be the correct diagram for wiring LEDs with different voltages?
No, that is not correct.
That will apply 18V to the all the strings.
9.6V strings of LEDs get 18V, and they get damaged.
It will also apply 18V to the 4.4V string with 100 ohm resistors, so 13.6 V is over the resistor and 136 mA flows in the resistors and LEDs. The LEDs will damage if they don't handle 136mA. The resistors will damage if they can't handle the 1.85 watts power dissipation.