If you are fine with a bit of a hacky solution I have found staples are often quite useful for this sort of thing.
If you have a stapler just staple nothing, collect the staple, and then unbend the prongs into the shape you need. Then just stick it in the slot and wiggle it about to try and lever the SIM card out. I think its unlikely you would damage anything since I don’t think the connections would be very sensitive.