You shouldn't have a problem with the water tank draining. The inlet and outlet are typically on top of the tank. You will get water out of the lines when they are cut, but you can minimize this by first opening several taps after the water is shut off at the meter. You don't have to open all of them, but try to locate the one that is lowest in the system. Sometimes I will flush one of my toilets once or twice depending on where I am cutting into the lines). You just want to get the dripping to stop so you can make good soldered connections. Leave the taps open while you are working, and shut them after all the changes are made and before the water gets turned back on. Then turn the taps on one at a time to bleed air out of the lines.

Also, if your only main cut-off is at the curb, I'd look at installing one where the water service enters the house. It's also a good time to install isolation valves so you don't, in the future, have to shut off the entire house to change a washer in the bathroom or laundry.
JM$.02W

@randy: installing shutdown valves involves work in the crawl space, which is beyond my abilities.

Thank you both for the replies.

I should have been clearer about having several taps open: one of them should be the highest point in the plumbing system, too.