Easy without a single knife stroke: trade knife for another apple

The woman puts the apples right next to each other so that they touch.
Then she precisely cuts off 1/4 of both apples in one stroke.
Each man then takes one of the apples, while the woman gets the 2 quarter pieces.

That way the woman gets 2/3 as much as a man, while doing all the work.

You position the apple so that cutting a straight line across both apples removed 1/3 of each apple so there are 2- 2/3 piece of apples and 2-1/3 pieces so everyone gets 2/3 of an apple. This is basic math and logic