Assuming this is a resistance welder, the voltage of the secondary will be of the order of one volt, and the current in the thousands of amps. That is, the power throughput will be several kilowatts for a fraction of a second. The transformer secondary will be one turn only, consisting of bundled copper strips perhaps 0.1mm thick, 15mm wide and the bundle several mm thick. This bundle needs to flex when clamped to the saw blade each side of the break when the weld is formed.
The blade is clamped with the two sides of the break abutting, and pressed together by a strong spring force. To make the weld, a timed pulse is passed through the break in the blade, and the material at the break is heated to melting point, and fused by the pressure. After cooling, a lower current is used to heat the join to annealing temperature. The flash is then ground back to give a uniform cross section.
The transformer is rated for a low duty cycle, perhaps 5% or less. In a similar garage spot welder, the transformer is soon very hot after a few welds, and is not suitable for fast continuous use. Welders in a car plant are liquid cooled. A band saw welder benefits from being able to cool during the longer time between welds.
Thus the transformer is a specialist design where the flux in the core is pushed as high as possible so as to need fewer turns, which can be thicker wire. A voltage changing transformer would almost certainly need to be bigger in overall size than the welder transformer itself. The welder transformer primary could possibly be rewound, but this is unlikely to be a simple matter. The wire will probably be square or rectangular section, and needs to fill the space to preserve the power rating.