Well, by airbrushed on, I'm assuming you're looking for feathered edges.
I don't know what kind of software you have, so I'll give you a couple of approaches:
1. If you have MS office, install Photo Editor. There's some tools in there to smudge or sharpen an image; you can probably use the smudge option to lighten up those edges.
2. (preferred) If you have some photo-editing software, there is often an option to start with a blank image in there, and then draw whatever you want... usually there is a drawing style that resembles a spray pattern. (even MS paint has this pattern, though it's not that good)
For example, look at this link: http://www.signweb.com/fabrication/cont/deuceswild.html
I believe the second image on the page was done in Photoshop, and it certainly looks airbrushed to me. I'm pretty sure Photoshop Elements can do the same, and wouldn't be surprised if other image editing programs were also capable of this.
Also keep in mind that inkjets (I assume that's what kind of printer you have) don't always do a particularly good job on edges anyway... if you tinker with the image resolution and quality settings, you may be able to tweak the image enough to give you those feathered edges without actually having to go through the trouble of working with the graphics software.