How to rewire a microwave exhaust fan to work as a stand alone exhaust fan?
You need to install a switch (toggle, rocker, paddle, etc.). Connect the Black wire from the plug cord to a terminal on the switch. This will be the Hot wire that carries the power to motor. On the other switch terminal you can either wire the Blue (for High speed) or Yellow (for Low speed) that come from the motor of the fan.
You should probably keep the Thermal Fuse as it may be protecting the motor and an integral part of the system. The Thermal Fuse is a safety device that has a bi-metal disc inside that connects the Blue and Yellow wires to complete the circuit. If it senses a higher heat than what it is calibrated for the disc warps and opens the circuit stopping the flow of power until it cools and snaps back and closes the circuit.
Always enclose a switch with an UL approved enclosure with a cover plate and wire clamps.
You could probably use a Double Switch [![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/tnIYd.png  so that the Dual Speeds will be available.