Hi @mandykelly
Doing this would mean having a cable permanently attached to the speaker which may be bothersome. It also needs to be tethered correctly so that flexibility where it leaves the speaker would be minimal ensuring that there's no strain on the cable connections in the speaker.
Other than that you may have to check what the current rating is on the adapter that you have now that you wish to bypass, to ensure that the replacement 12V supply can supply the same amount of current and not less.