Unicorn nightlight battery pack

This is a battery pack for this nefarious night light with one 5mm led that runs with 3 1.5V LR44 batteries. An educated monkey crunches the numbers quite easily, getting an idea that this piece of..nightlight runs only a bit over 1 week with 3 small batteries.

My daughter received a pack of 2 of these as a bday present and of course i had to do something about this, (I don't want to spend ludicrous amounts of money for the batteries), so i designed a battery pack for 3 x AAA rechargeable ba