It will work, but slower and you will raise the amp draw by the lower voltage output. Not real bad on the scale of things . Also if you check the output of the 12 volt it may already be in the 13 or 14 volt range as the standards are not to tight on dc voltage. Like in your auto , 12 volt system but when you look at the output it says 14 volt .
One thing you really need to check is the pin out and make sure the center of the plug is + or - is as it is needed for your battery pack .
You can get a cheap one at Wally world that will put out multi voltages and have the plugs that you need for you machine . I would check that also .