But to get a signature that looks realistic you will normally need a consistent colour, in your screenshot above the 'signature' itself has blue and white pixels;
That screenshot shows the result after saving to png (from jpg). The writing is only blue, a blue pen. The background actually pure / a single white (a sheet of paper, DIN A4). So actually the writing must be pure blue, the background pure white, two colors. Yes, now it looks transparent:
Another completely different approach, on which I can't give advice, might be to vectorise the signature to produce a smooth outline, maybe using a software like the freeware Inkscape. But then you would have to consider how you intend to use the signature, which hasn't been discussed.
You mean, in what programs? I want to try use it in pdfs, docs, odts, so pdf / writing programs. I assume, with the image / signature saved with XnView this will work. So actually this should be enough.