No nothing will happen over your fingers.
On an open wound, or your tongue in this case, it will hurt a bit (a bit is qualitative as some people's bit is different to others). You shouldn't die.
Transformers are good =]], the only slightly problematic thing is - like everything else, when you run them at full power for a long time they get hot, but other than that, there is nothing to worry about it.
The X-former in your wall supply will be followed by a bridge recitifier, capacitor(s), voltage regulator and current bypass - unless it is a switchmode supply then it's different.
Power supplies are good, you will be surprised at the amount of money you save on batteries. Invest in a "bench supply" at some stage, they are good too.