Based on casual use of a small spot welder I would recommend an empirical approach, there are variables to the process including prep, force, material and desired service duty factor.
Most welding processes become much more controllable and repeatable from a stable current source. MIG welding being a notable exception.
Something that tends more towards having a higher impedance constant current output rather than a very low impedance constant voltage output. High impedance being relative of course ! !
The traditional method for making a constant current transformer is to place a shunt magnetic air gap between primary and secondary. In the case of the ancient "buzz box" stick welder, the shunt gap is adjustable with a slider rod. Something like that perhaps, but wound with a much lower secondary voltage.
The key to transformer design is deliberately increasing the leakage inductance by reducing the direct primary/secondary magnetic coupling. Windings side by side, not one on top of the other.
Even better with a deliberate shut magnetic path around the primary.