>5v at 2A
> 10v at 1A
Very awkward.
I wonder if the "10V" is really a cheap 12V. This thing is a CD player (among other things), right? CD transports often ate 5V and 12V, standard PC voltages. However they would (usually) work with less of the 12V (perhaps slower, which seems to be a comment).
5V/12V supplies are or were VERY common for external PC drive cases.
As you are not sure this particular unit can eat 12V, and 2V is a slim drop for many regulators, I'd consider three 3A rectifier diodes in series between 12V and 10V. (I've run a few 3V systems on 5V this way.)