You could put a loop system that circulates the cold water from the pipes back through the heater for a set amount of time, then have it switch over to sending the water to the shower. The problem is that a set of pipes will need to be installed that can send the water back and may need a custom solution on switching from circulating to dispensing. In the long run, it would be cheaper, but it would take a fair amount of time to pay itself back. The positive is that it is cheaper than installing electric heater on every water outlet but more expensive for just one outlet.

As you said, the pipes are not easily accessible. You may need to just live with it or suck it up and pay the professionals to install either the whole house water scavanging system for every hot water tap to be hot or just an electric water heater for just the shower. Depends on how much you want to save water vs. how much cash you can throw at this problem.