I can't speak as to how a fancy 10W divelight would work, but in cheap crappy 35W HID lights, you give the ballast 12V power, with enough power available, and the thing turns on and lights the bulb. Remove power, light turns off.
If the switching circuitry isn't built into the ballast, i.e. if you can remove ballast, bulb, reflector and verify that actuating the power switch does indeed switch the ballast power input on and off with no ballast present, you should be able to use any 12V drop-in. Keep in mind, though, most 26.5mm drop-ins are designed for "P60" flashlights, and most "P60" lights are ~6v max (2x 3V CR123a cells). The output voltage from the ballast settles in around 85V for a typical 35W HID, but strikes the arc at ~24,000V. So, you'll definitely not want to just replace the HID bulb with an LED.
Are you just not liking the 10W HID? Could it be that while the battery has been tested fine, the bulb is old? And have you been able to crack it open and look at its guts yet? My main concern is that the ballast might also contains fancy charging circuitry for the battery, and switch circuitry that would be required for the light to still function, in which case, removing the ballast would not be an option.