It is 16-volt AC. So, almost any tranny will work as long as it can do 1 amp. But you want to make sure it does a little more than that. Like 2 or 3 amps. You don't want to run a tranny at it's limit.
I also have the Twin Tube Classic. It's one of those pedals that I doubt I'd ever sell. They do something kinda cool internally. They have a 240 volt to 16 volt tranny, wired backwards. So it takes the 16VAC and drives it back up to 240 so that the tubes are run at true HV. I believe that's what gives it the "true" tube sound. It's not a starved plate design, like my Vox Tonelab. (Even though I love my ToneLab.)
But have you contacted Duncan. I did, back when mine went bad, and they just sent me a new Walwart. (If they still have them.)