Setting transparent images background in IrfanView

You were on the right track. IrfanView sets the background for transparency the same as the viewing color around the image.

You just need to re-open the image with IrfanView after changing the view color to white.

To change the viewing color in Irfanview go to:

Options > Properties/Settings > Viewing > Main window color

If you are using the batch conversion, in the window click "options" in the "Batch conversion settings-output format" and tick the two boxes "save transparent color" (one under "PNG" and the other under "ICO").