Tried. I even thought about the 4.2v charger modules to replace the original board
You should be able to build a charger from a dedicated 4.2V charger adaptor and a headset kit or the ones on you knackered charger. You can get these off ebay and they come with a jackplug which you would remove and solder the wires direct to the correct terminals in your knackered charger. I converted a lead acid rack charger to charge Li Ion by replacing the PCBs with dedicated Li Ion.boards. I may have posted about this on aditnow. Only thing to remember is that is a one to one, that 1 board to each charging station unles the boards a dual output. So your adaptor off eBay would have to charge one single lamp. There would also be an issue with chage time as the DL16 is 16 AH as its name suggests. So it has an array of parallel cells and each would only receive a fraction of the charge current. The genuine Oldham chargers run a fast charge system that is different to the usual constant voltage system used for Li Ion. I am not at all sure how this works.
As far as modifying you existing, it would possibly be simplest to remove the PCB and wire the clips to a female jackplug, but be sur eto check the size first,
One word of caution about some electronic stuff from China. Modern chargers use a switch mode power supply but still need an isolating transformer to ensure that if anything went wrong you could not get a mains in - mains out situation. I have yet to see one without this essential feature though, so this is possibly just my own personal mistrust! LOL. The mains adaptor chargers on eBay are OK, I have used them.