I can't tell what the OP's doing here.

If you are spending your wife's SkyMiles to purchase an award ticket, she will get a "congratulations on your SkyMiles award" e-mail to the address on her account.

If you are purchasing a ticket with money and/or your own SkyMiles, she will not get an e-mail unless you specifically list her e-mail address when making the reservation. That said, if her number is on the reservation, it'll show up if she logs into her account (online or in the DL app) for any reason. As already suggested, if you want to play it really safe, leave her SkyMiles number blank on the reservation and fill it in at check-in.