"Class II" and "Double Insulated" (same thing by the way) are IEC appliance circuit designations, the Class II is not exactly the same as Class 2 is here in North America. An IEC Class II circuit means that everything in it is double insulated, which means basically that no single failure will result in exposure to live electrical circuits by the user, AND that the devices are used WITHOUT having to have an earthed (grounded) frame. This is as opposed to a Class I circuit that requires earthing and using an RCCD (the equivalent of a GFCI for IEC countries) in the power circuit. Using a Class II transformer is only valid when ALL devices down stream of it are also Class II. In other words the designation is for the CIRCUIT, and to get it, all devices in the circuit must carry the designation, or be of low enough energy to not need it, i.e. battery powered. For that reason alone, Class II tends to only apply to small appliances such as cell phone chargers and other wall warts.
It's unlikely that you will find a transformer of that size with a Class II designation here in North America. Although transformer mfrs here make IEC versions of their products to go on export machinery, attaining something that stringent on a larger transformer would be very expensive and if you don't have enough market demand for it, uncompetitive. If it exists at all (because of how it must be used), only one of the larger IEC mfrs will have it. Then, it's not likely to have a UL listing, if that is going to be necessary as well.
