How to make an Arc welder out of 3500v bug zapper transformer?
You mentioned replacing the secondary with 10-gauge wire - I'm guessing that you have some understanding of the thicker wire's greater current-carrying capacity, which you would need for an arc welder. 

The problem here is that the magnetic core - the steel laminations - also have a maximum magnetic flux carrying capacity, just like the wire has a maximum current-carrying capacity. The bug-zapper manufacturer would have used the lowest-cost (smallest) laminated core that met the power needs of the zapper - which are MUCH less than what you'll need for an arc welder. You would find that the secondary current would max out at a too-low value.

One caution - if you do get hold of a microwave transformer, DO NOT power it up on the bench top. Microwave transformers are one of the few devices that supply both high voltage and relatively high current - and are pretty much guaranteed to kill you if you get across the HV side.  Not sure about bug zappers, but I'd be very cautious with that as well.