As no other answer yet.
Look at the components after the transformer. You might find a voltage regulator, which by its number, will give you its output voltage, You can then check online for its specs, (just search for it's number) which will give you the range of input voltages. As long as the output voltage of the tx you look for, is within that range no problem, Just then have to check the current rating required. You seem to know what you are talking about, so should be able to sort that out.
BUT failing a voltage regulator, I would start at 5V, being the voltage used by most mains powered units, (battery tend to run at 3.3 or lower.) I would think the maximum to be about 12v. Again being normal. So if possible get a multi tap Tx. step up until all works, But be careful not to jump too many volts in one go. Hope this helps
SD, June 2012