Are solenoids/inductors dangerous to have exposed?
At 9V I wouldn't worry about touching the solenoid.  After all, you can touch other parts of the circuit that are at 9V.

The only issue with a solenoid is that it can for a short period of time make a high voltage if its current is shut off suddenly.  For example, hold the wires of a solenoid accross a 9V source, then watch what happens when you release one of the wires.  You'll see a spark.  This is indication of temporary high voltage.  If you were touching the two wires at the time you'd feel this spark.  But, its energy is limited and duration short, so other than being unpleasant won't do anything bad unless maybe you somehow manage to get the current running thru your heart or your brain.

The same temporary high voltage you can feel can also damage your circuit if you don't deal with the stored energy in the solenoid properly.  The simplest way to do this is to put a diode in reverse accross the solenoid:



In this case transistor Q1 is just a example of something switching the solonoid on and off.  L1 is the solenoid coil, which is just a inductor with significant series resistance from the point of view of the driving circuit.  D1 is reverse biased and therefore does nothing when the solenoid is on.  However, when the solenoid is switched off it provides a path for the current to flow until it decays by disspating against the inherent resistance of the solenoid and the voltage drop accross D1.  The highest voltage ever in this circuit is 9V plus the forward drop accross D1.  This circuit would be safe to touch with your hands like any other 9V circuit.