I found this article about how many calories it takes to click a mouse (I'm going to hazard a guess that it's about as hard to click a Di2 shifter as it is to click a mouse):
https://mashable.com/2013/03/13/mouse-click-calories
"On average, 16.7 micromoles of ATP (Adenosine triphosphate) are consumed in moving one gram of muscle for one second. So, the total amount of ATP burned to move 11.7 grams of muscle in the index finger is approximately 195 micromoles (11.7g×16.7μ mol/g). There are 7.3 calories in one mole of ATP energy, so the number of calories burned in clicking the mouse equals about 1.42 (7.3/1000) X 195)."
However, it appears they managed to screw up the math. A micromole is *one millionth* of a mole, not one thousandth. So the result is not 7.3 X .195, it's 7.3 * .000195, or .00142 calories. So 1000 presses of Di2 would require about 1.42 calories.
Since it requires moving your entire hand to shift a mechanical shifter, how much energy does it take to move your hand? Well, the human hand weighs about half a kilo. (Don't ask me how I know.) Your hand is about 500/11 or 45 times bigger than your finger, so it would take 45 times more energy to move your hand. So to shift a mechanical shifter 1000 times would take about 45 * 1.42 calories, or 63.9 calories over a century ride. (We burn about 600-800 calories an hour cycling, so that sounds about right.)
That's a little less than one slice of bread. So instead of springing for Di2 for your wife, just give her a slice of bread before the ride, and you'll both be on equal footing!