Not sure what Class II refers to, but RS's "adapter" is also a transformer because it reduces line voltage (120v or 240v) to low voltage (12v) needed for most electronics. You'll also have to verify the polarity is the same as your old one (look for a symbol with + and - symbols pointing to the inside and/or outside of the round plug, though not sure if correct polarity is crucial if it's only powering a lamp) and that the output amperage (in amps or milliamps/mA) is the same or higher than the old one.