I grew up in the early 70s with one of these in my bedroom, probably from the 40s or 50s but still going strong. I never stuck my fingers into the blades, but I did like to toss crayons in and watch the pieces fly...

I took some 120mm fans out of some old servers my brother brought home from his tobacco factory co-op job.

I’d wire them to weird voltages (e.g. 12V and -5V, or +5 and -5), cover my eyes with a jewel case and drop small screws in them to hear where it bounced around incredibly fast...

My grandparents had a completely open fan from the 60ies (although with plastic blades). You could stuck your fingers into it and it would just stop - it hurt a little, but no damage.

I don't know about the torque on the desk fans. But modern ceiling fans have very low torque and kinetic energy: you will probably get away with sticking your hand into one of them with very little damage.