Do I really need to call the utility company just to turn off the water
main?

Do you absolutely, positively "have to?"

NO.

It's a VERY good idea. First, they might get upset if they catch our
fooling around their meter. Second, (as another poster noted), if
something "goes wrong," someone else will likely pay for it.

Frankly, this is one area where it would pay you to pay a professional
plumber to handle the whole thing. With a good shut off valve you can do
almost any plumbing in your house without risk.