Well, I had to use the new phone somehow, so I didn't have much choice. Found a good illustration with exact dimensions - it seemed easy to do. So for a test object I found an old Rogers SIM card, which I didn't need anymore, got good scissors, did the measurements, and just cut the card.
The new card could fit into the phone, and it did not complain.
So, I got my working Wind SIM card, and again measured it. I was afraid its bigger chip would be too big, but it looked exactly the right size! A couple minutes later I got a home-made micro-SIM card:
Put it into the phone, and ta-da! It worked!
So it is confirmed: you can actually make a micro-SIM card from a regular SIM without any special tools! You just need a ruler, regular scissors, and a pair of straight hands.