Unless you know more about the specific "wall wart" and/or the device in question, it's not necessarily safe to assume that a much higher current rating (for the wall wart) fundamentally can't cause problems.

If the wall wart is truly a regulated DC power supply, that's great - it can deliver very close to the specified voltage at pretty much any load within its working range.

Many wall warts, however, are unregulated, and the voltage depends on the load. If you're loading it such that the current draw is substantially less than the rating, then the voltage will be higher than what's specified on the wall wart. If you have a meter, measure the no-load voltage on some wall warts some time - or look at Graph 1 in this article to see one example.

If you're using an unregulated wall wart far below its rated current, then you're back to what Angel was talking about - it depends how happy the device is to be fed voltage higher than it nominally requires.