Not really. MS Paint doesn't use antialiasing, a fancy way of saying smooth (non-pixely) outlines or layers. There are a couple of things you can do to help, though. The first is just use a white background or white-backgrounded boxes for your sugimori images in signatures or avatars. The second, and more effective, is like Rubypoke mentioned: go through and draw in an outline by hand, and erasing any white bits that fall outside it:
This effectively lets you work with a non-pixel image as a pixel image, because it has a pixeled outline.
Or you could get a program that allows for antialiasing, like Gimp, which is free.
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