The only case where Ti wire has any advantage over Al wire is when you intend to make the electrical connection to the work via spring tension. This is because titanium can be hardened and tempered to a much higher degree than any alloy of aluminum. With this in mind, you want Ti wire with the highest spring temper that you can find.
M_D has advised that the Ti wire Caswell used to provide is too soft to provide much spring tension. Ask your supplier to recommend an alloy with the best spring characteristics.
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