Sounds like a plan but if the plants have been exclusivly under lights bring one to the patio if plants appear unhappy within two days.

Have a plan for excessive wind / thunderstorms during hardening off period.

The temperatures ( 50F ++) is just fine.
Now if you keep them in the shady place, there is no need to cover them with shade cloth. A couple hours of morning sun should be ok to start.

One more thing: Can you keep your basement cooler for few days before moving your plants out ? For example by opening windows (if there are any).
But all in all min. temp of 50F should not be too shocking, especially when you bring them out in the morning when it starts getting warmer out side. The purpose of hardening of it to avoid big changes in temperature for a few few days until the get used to it. Tomatoe can tolerate temperatures as low as 37F, provided it is done gradually. But in your case 50F is nothing to be concerned about.

Sey