I can't really help you use a touch screen without touching it.
Keep your hands clean and dry? Wear e-tip gloves? Get one that accepts stylus input.
You raise an interesting idea with the touchpad with tiles display. This could be achieved with a Windows 8 tablet or tablet convertible. Lay it flat on your table, connect keyboard and a secondary non-touch screen monitor to it. Use the tablet screen as a touch pad.
The only problem I see is, depending on what you want to do, the Windows 8 tablet may be underpowered and / or overpriced.
Personally, I would just lay off the meatball subs and cheetos while I was working on the touch screen and keep a micro fiber cloth handy to occassionally wipe the screen.
Keep Up with TechRepublic