In psp If you add a mask layer It on its own is not a alpha channel If you delete the mask it will ask if you want to merge if you say yes you now have a image with transparency just the same as if you had used the wand to select and remove the white.

If you add a new layer and move it to the bottom you can fill with colour to see how the transparency appearers on each Background Colour

Png can store partial transparency unlike gif that only instructs the programme not to paint the white.
Depending on your use for the image saving as PSP or PSD my be easier