You need a wall-wart that has an output of from 3VDC to 6VDC at 1A. A 5V one is common. It feeds an LM317 adjustable voltage regulator set for an output of 1.2V to 1.5V. The LM317 will need a medium size heatsink if the wall wart voltage is higher than 3V. The datasheet for the LM317 shows its circuit that has important input and output capacitors. For an output voltage of 1.25V just one wire from its ADJ pin to its output pin sets it but an adjustable voltage output requires a resistor and a potentiometer.
It may be hard to find the simplest solution which is a 2.4V 1A ~ 2A wall supply. and matching DC jack.
The motor is rated for 1~3V with 2.4V nom. with <1A nom and 4.5A startup. Not having 5A supply just means it takes 5x longer to start up.
The best solution is to keep the hair clipper running from its battery and use a charger for it.
Rechargeable batteries and chargers are available on the market and safe in use.