I found that skinstudio was making a bit of a mess of a recent conversion I tried so I had to use photoshop. It was a bit of a journey trying to get photoshop to comply, I would convert the image to 16 colours indexed mode but then when I went to save it I wasn't offered the opportunity to save it as a 4 bit image, only 8 bits.
In the end, if I remember correctly, I had to change it to indexed mode, 16 colours, with black and white as forced colours in the palette - then when I went to save it, both 8 bit and 4 bit options were available.