Is it possible to quickly switch between attack types?

No, there is no way to switch between these skills with the same input. You can equip both of these skills, however, to separate keys (left and right click, or left click and a hotbar slot, for example) so you can still quickly switch between using them. See here for more information on doing that.

This is very different to how skill selection worked in Diablo 2, so if you're familiar with that game it will take some getting used to. If you're not in town, swapping out skills in Diablo 3 has a cooldown where you can't switch skills again or use the new skill, specifically to prohibit what you're going for.