The component of the nervous system that is the last to be involved in the process of swatting at a mosquito is the axons in motor neurons.
When you see a mosquito land on your hand, sensory neurons (which include dendrites in sensory neurons) detect the stimulus. This information is then relayed to the spinal cord and brain, where it is processed. The motor neurons then send signals to your muscles to execute the swat. Therefore, the axons in motor neurons are involved last in this sequence.