Just ask for an extension. Professors have seen this "trick" a thousand times and know exactly what you're doing. They will respect you more and give you more leeway in the future if you're straight with them.
I am not against taxation. I am against MANDATORY taxation. Do you honestly think that giving people a choice is a bad thing?
No-one wants mandatory military service, but it's necessary for the sake of society as a whole. Maybe one day it won't be, but clearly that's just how things are now.
As for choice, you do have a choice and you know it. Civilian service is a thing here.
We have military service here because we're a small country with a large and aggressive neighbour that not only has attacked us within living memory, but is currently demonstrating what it does to neighbouring countries that it thinks it can get away with attacking.
If you're going to memorise a deck of cards, you're better off learning something like the Mnemonica Stack as you can use it as the basis for a whole load of card tricks.
Just ask for an extension. Professors have seen this "trick" a thousand times and know exactly what you're doing. They will respect you more and give you more leeway in the future if you're straight with them.