But can e.g. 3V DC kill? Perhaps by using the body's resistance, but I have the idea that the effect would be different from say 220V AC, which affects the nerves.
Not generally, remember Ohm's Law I = V/R. Internally the body has a resistance of ~300 Ohms as a rough rule while our skin is 1000-10000 depending on the condition and contact area involved.
So 3V isn't going to pose any real risk unless it's applied internally and right across a critical nerve leading to your heart or a muscle directly on the heart. For reference pacemakers are generally set to 2-3 volts. Applied externally up to ~12V is generally considered low enough voltage there's a low risk of truly adverse effects.
10 milliamps across your heart can kill but using Ohm's law we can calculate 3V / 0.010 A to get a resistance of 300 ohms. This means you're probably still going to have a bad time if you apply it directly across your heart during open-heart surgery but other than that 3 volts just isn't enough to drive a lethal current through your skin.
Which is why if caught in a lightning storm you should crouch with feet together and why I try very hard to only use one hand when doing something that might have the potential to shock me.
Depends how it's applied and what's sourcing it. 3v does basically nothing to dry skin, but would be quite bad on wires implanted in your chest across your heart.