Can I use thicker pastry dough in place of fillo / wonton wrappers / lumpia wrappers? I just concluded making bourek (sp. var.) yesterday and everyone commented how great it was.  I have also made the Filipino appetizer lumpia, and some sort of triangle pastry with pine nuts (I forget the name), using wonton wrappers in recent past as well with some success.  

But my greatest anxiety in cooking (more than anything, including deeply cutting myself with a 12 inch dull blade when I am chopping) is working with this very thin fragile dough.

Can I use a thicker dough for such a recipe?  Is it entirely necessary for the dough to be paper-thin?  Is it a taste thing?  Why is it necessary to use this dough for this type of appetizer / dish?
Phyllo dough, in particular, comes in several thicknesses, from the thinnest which is used for baklava up to horiatiko (country) style which is used for rustic pies. You can substitute, but there is definitely a noticeable difference and I think you'll appreciate why a good traditional recipe calls for a specific type. Saveur has a nice reference chart.

Also, keep in mind that although phyllo is very thin and tends to tear, in many cases a small amount of tearing is no problem. You are making multiple layers and any small imperfections will disappear. Just be sure to keep the pieces you aren't currently working with covered so they don't dry out too fast.

For wonton wrappers, they are also often available in at least two thicknesses in good Asian groceries. Again, there are traditional uses for each. When using them in a non-traditional context such as ravioli, you'll have to decide for yourself which you prefer.