It's easily available, and perfectly safe to use (although a bit hard to clean up).
I recently went to sleep while chewing a gum, and woke up in the morning with my head "stuck" to the pillow. I had an almost bottle-cap sized patch of hair tangled up in the gum.
After pondering the internet for advice, I ended up using vegetable (cooking) oil, although the Olive oil is recommended. I soaked the exposed area with an old toothbrush for 5-10 minutes, and then just combed the gum out and washed the hair a few times with the shampoo (the oil is really hard to get out).
It's messy, and your skin will hurt for a bit near the hair roots, but you will be gum-free. And it beats the solvents by a long shot.