Hi Epodandy,
Welcome to our forum.
You could use a CD4017 or CD74HC4017 (higher output current)stepper to select the LEDs, and a monostable circuit to de-bounce the button. But it will need a step-up voltage converter to light 3.5V or more blue, white or purple LEDs from only 3VDC.
Yes, purple. I was sent some substitutes for the blue LEDs that I ordered, and they were the new purple ones by mistake!