You don't need a constant current power supply, an ordinary power supply with enough voltage and current will be sufficient.
The LDD700 produces a constant current of 700ma for the LEDs. When you select the voltage remember that the LDD700 drops some voltage. Check the data sheet but it is probably around 1.2 volts, so make sure the power supply voltage is higher than the sum of the forward voltages for the LEDs.
You mention having strings of ten LEDs with a forward voltage of 3.4-4v, so a total of 34-40v per string. You're probably better to get a higher voltage power supply, say a 48v supply.
The LDD700 produces a constant current of 700ma for the LEDs. When you select the voltage remember that the LDD700 drops some voltage. Check the data sheet but it is probably around 1.2 volts, so make sure the power supply voltage is higher than the sum of the forward voltages for the LEDs.
You mention having strings of ten LEDs with a forward voltage of 3.4-4v, so a total of 34-40v per string. You're probably better to get a higher voltage power supply, say a 48v supply.