A lighted fans is really two devices in one unit. There is a FAN MOTOR, and separately some LIGHTS in the frame. The MOTOR requires power at 12 VDC (max) and also includes a way to send back out its speed signal. An 3-pin fan has its speed controlled (reduced) by reducing the VOLTAGE supplied to it on Pin #2 (Pin #1 is Ground). A newer 4-pin fan must have a special PWM Control Signal supplied on Pin #4 to control its speed; otherwise (with no such signal) it will run full speed.
Power for the LIGHTS AND control of their display pattern is done separately from the motor. If no connection is made to these inputs, the lights simply will not operate. For ARGB lighting systems, there are three inputs: Ground, +5 VDC supply, and the Digital Control Line carrying data packets of instructions. Normally ALL of these are supplied from a Controller, either one on the mobo that feeds these signals out on an ARGB Header, or one in a separate ARGB Controller Box that requires at least a 5 VDC power source and Ground, plus some means of issuing configuration settings to set the display.
For simply cooling this laser enclosure, OP should be using a simple fan with NO lights. This would require a modest power source of 12 VDC at up to 1.0 A max current for almost all fans designed for computer case use. Very high-performance fans for larger applications can be had but may need a higher max amps rating. With no other control systems, such a fan will operate at full speed always. Fans of the type OP cited CAN be used with custom connectors arranged for the MOTOR only, but that wastes the ARGB lights that cost money. IF OP wants those lights to WORK then a second power supply and Controller will be needed, and that's getting complicated and more expensive.