Truth is, if you're interested in doing this all with a button click, you don't need the pivot table at all. Much easier to just write the 'filtering' into the macro. That's easily the cleanest way to do it.
I was thinking the same thing. A simple macro can easily be recorded to do the following steps;
1. Copy the full order form (A:B)
2. Create a new sheet and paste the data
3. Add filter and filter all the 0's or blanks
4. Delete all those rows and unfilter
-end recording
This leaves you with just the items and qty on the order.
After recording you can add a button and assign it to this macro and it should be simple enough for any user.
I didnt get a chance to test it yet, so it may need a minor tweak, but it seems to be the simplest option to me.