Andy writes:

Remember, you are going to have to have an external pump
to do this because the pressure in the cold water line is the
same as the pressure in the hot water line.

To have instant hot water, the pump must operate continuously.
This is a valid technical solution to your problem, but a costly one.

I would suggest that you put a flash hot water heater at the
point of use. That way you wouldn't need to use energy until
you are ready to use water.

On the other hand, 4 litres of water doesn't cost much. It is
about the same as flushing a toilet.

In my house, I have installed a smaller hot water heater
in series with the hot water line at the point of use. It doesn't
work nearly as well as a flash heater, or the recirculating
pump that you propose, but it works well enough....

Just some suggestions...

Andy