It not that we don't want to answer with such specifics, but swapping an internal transformer for a properly spec'd new one is something that anyone familiar with electronics should be able to do, by simply calculating the power consumption (it states right on the back of the boombox on data spec markings), and the desired voltage output of new transformer. So many new transformer choices from so many manufacturers from so many distributors.......
Then you'll need to physically measure the space available, the mounting screw spacing, etc. etc. YOU must do that since the S90 isn't really a common boombox as it was never introduced in the USA. You can't really expect someone else to go through all that trouble of taking apart their boombox to do all the legwork for you. Comparing the aforementioned data collected with the datasheet of the new products is the way to choose an appropriate one.
Finally, unlike low voltage applications (12v, 15v, etc.) transformers are high voltage devices with lethal potential. NO ONE unfamiliar with electronic basics should attempt to work on that portion of an electronic device unless they are familiar with such projects for reasons of safety.
Since it really sounds like you need a lot of guidance here and not that familiar with electronics, it's best that you simply use the appropriate adapter options already recommended and mentioned elsewhere in this thread rather than pursue replacing the transformer unless you intend to farm the work out to a professional. From the factory, almost all boombox power supplies insulate the primaries so all exposed metal within the boombox is low secondary voltage only. This is for safety reasons. Otherwise, a grounding plug would be required. If you don't know what you are doing, it is possible to circumvent those safeguards that were built into the boombox and the device might appear to work fine but can introduce potentially dangerous conditions for you or future owners of the boombox.
There is one more option which will work for you but since you already sound lost with a transformer replacement, which is about as simple of an electronics upgrade as can be -- it wouldn't interest you. But rather than replace the transformer (which would output more voltage than intended due to higher than intended voltage IN), it is possible to build and insert additional circuitry between the transformer and the mainboard. I'm talking about a voltage regulator circuit which will "regulate" the higher voltage to the desired 15 volts that the boombox wants. However, like I said, this would be even more complicated than replacing the transformer.