It should work, but the whammy DT should come with its own power supply. According to the manual it should be in the box.
But if yours is missing, the Boss PSA 120S should work. It has the standard polarity center negative barrel and plenty of ma and it puts out DC just as the whammy dt requires.
You can ignore the power requirement printed on the pedal. 1300ma. Woah.
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Their own manual says different saying 288ma.
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When I was researching the actual power requirements a couple years agos I found this on the voodoo labs forum. Sadly, that forum doesn't seem to exist any longer when I just searched for it. I'm glad I saved this screenshot. It says actual current draw is less than 250ma according to voodoo lab tech support.
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