convert a mains LED clock to battery

Hello,

I have a small project I am doing and could use a little advice. I want to convert a LED clock that currently runs on 230v mains to run on battery. I have a infant son who is sleeping in our room at the moment, when he stirs at night I would like to see what time it is, currently illuminating the phone to check the time is too bright and often wakes him fully. As there is not enough sockets in the bed room I thought to convert a simple cheap red LED clock to run on battery.
I opened the clock and the ac mains cable goes through what I can only assume is a step down unit, it appears to be a coil of wire?, heavy enough anyway. I ran a volt metre across the input where it is soldered onto the circuit board and it reads as 6.3v (if I am doing that right)
So what to do to next to be able to have it run on a 9v battery for example.
There is a battery connection for a back-up for the clock, but it appears that this only keeps the time without the clock display being illuminated. If I set the time, un plug it for 30 mins, then replug it in, the time has moved on 30 mins but the LED display has not been on.
The only other information I can gather is from a sticker on the case that says power "Power source: AC 230V - 50hz
DC9V battery back up for clock.
power consumption 3W/hour
standby consumption 1.7W/hour."
I appreciate any help that can be given.

 

Thank you both for your replies, unfortunate I cannot (or would not be practical) to do what I had hoped to do and shall look else where for a solution to the problem. Another purchase, perhaps on of the recommendations.