Husks/skins can be removed before planting, but only *just* before; never remove them before storage.
If you have had problems with thrips in the past, it can be helpful to remove the papery husks and treat the naked corms with Sevin by putting corms in a paper bag, adding a generous dusting of Sevin dust, shaking *gently* to coat, and then planting between 12-24 hours later. Don't leave them naked for longer than that, though, or they might lose too much moisture, and never remove the entire husk before overwinter storage -- you can remove the loose old husk, but the newer, lighter-colored, and more tightly-wrapped husks should remain.
No, do not remove the skins from the corms.