First of all, someone "skilled in the art" might be able to fix your charger. Could just be a blown fuse or burned component. As for your other question about battery types, technically the different chemistries have different charging profiles, however they all need more than their nominal voltage to charge, and as long as your power supply is not too big compared to the batteries, it should be fine. For example, Black and Decker sells a charger for both their NiCd and Lithium Ion VersaPak batteries (silver and gold) and it is nothing but an unregulated DC power supply. The transformer loads down, since it is small, and that prevents over charging. They charge their 3.3V batteries up to about 4.3V. So that is why a cheap unregulated wall wart supply is a good solution. It will float up to around 28V which is what you want. But if it really was me I would just fix it since that is what I do.

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra