Analog latency in an opamp circuit
It can easily be done, but the target criterion must first be specified.

For example, if the target criterion is the difference in time it takes for current in the loads to rise to 1 milliampere from the time the leading edge of the pulse first hits the loads, then that difference is the latency of which you speak.

In the graphic below, the incident pulse is shown in black, the LED response in red, and the speaker response in green.

The figures are imaginary, but serve to illustrate the concept.