Is it safe to shut off cold water entering water heater?
If you have no separate shut off valve you should wait till the local water authority can come and temporarily shut off the water at the meter (which is presumably near the street).

I see no problem with shutting off the water supply to the water heater as a short term measure to curb the water waste from the leaking faucet in the shower. It would be a good idea to turn off the water heater during the time that the water supply is turned off. 

After you turn the water supply back on the only issue you will have with the water heater is that some air could have fed back into the tank. All you have to do is to open the hot water valves in several of your sinks and let them run for a short while until the water runs clear without any bubbles or spitting coming out of the faucets.