Is it dangerous to do a skidding turn to lose altitude without increasing airspeed?
As Ron Beyer pointed out in a comment, your instructor was showing you a forward slip - a pretty standard maneuver for light aircraft.

A spin would involve full rudder and a stalled wing, which usually means pulling the yoke or stick back a lot.  That's why overshooting the base-to-final turn can be dangerous - you likely already have a lot of rudder in and it's tempting to pull back on the yoke to try to tighten up the turn.  An unexpected spin at low altitude is not recommended as recovery tends to be both abrupt and fatal.

As long as you're keeping the yoke more or less centered forward and back and your airspeed up, there should be nothing to worry about.