If you're talking about a controlled situation where you need to provide a given amount of power - ie driving the accessories of a car, then yes, a lower voltage would require higher current. P = IV
When you're talking about safety though, the issue is what happens if the voltage gets applied to your body. In that case the relevant formula is I = V/R. R is the resistance of whatever circuit you've mistakenly formed through your body. The higher the voltage applied across that circuit, the higher the current that will flow. (This is also why it's more dangerous if you're wet, or in bare feet, for instance, because those things lower your resistance, resulting in greater current for a given voltage.)