Can I use a TRIAC on a secondary isolated AC winding?
A simple answer is "yes you can". The better answer is "you don't have to", because in your situation, it is better to use a triac control on the primary side. I have seen many special heating devices that use this approach, the current is smaller compared to the secondary, so you will not have trouble with short circuits where the major resistance would be your triac, thus the spot welder will heat mostly your triac and not the spot. 
Forget about using a zero cross detector circuit, the worst case for a transformer is to turn it on at 0V and don't use the 1.9T toroidal transformer (this is what you'll get in a shop for hallogen lamp), a use transformer designed with max. flux 1.6 Tesla or maybe less in order to keep dI/dt manageable.