Sounds like you want an infrared touch screen. The concept is pretty simple - a grid of IR emitters and receivers in the X and Y directions detect breaks in light corresponding to a touch (pictured below)
Because it doesn't work on contact electrical phenomena, you can use pretty much anything to break the beams including a gloved hand, a pen, your cat's paw (cat willing, of course), etc. Moreover, it's inherently multi-touch capable.
Infrared-based touch screens are also neat because the infrared sensor frame and screen can be discrete, so if the screen is damaged, you only need to replace it and not the touch module (and vice-versa).
Now, as to whether or not this is a desirable, feasible, or cost-effective solution is arguable, but if your requirements are rigid and you absolutely need a touch screen, then it may be your only turn-key option.
An alternative to the grid-based IR touch screen is one which uses "Frustrated Total Internal Reflection" whereby infrared light is projected within the display itself and "captured" via total internal reflection. A touch (or multiple touches) on the screen causes light to scatter from within the screen to a detector that captures the touches. This schema is depicted below:
The concept is simple enough that there exist a number of guides explaining how to build your own multi-touch display at a relatively low cost. For example, the source of the images above links to a wiki with instructions on building your own, and a cursory search on Instructables turns up 4 projects with instructions. Handling things like palm detection, gestures, etc., becomes primarily a software and image processing problem at that point.