First off, I recommend using the civilian core because it doesn't have the giant blue dot that doesn't shrink(I/K). Second, its very simple to turn a ship into a single section fighter. Just create a bitmap that is completely black and set it as the background, then zoom in on what you have built till its as large as you want, and make a screenshot. You can then save this as a .png(must manually make it lowercase unless your using something like photoshop) and place it in your custom sections folder.
Once you've dragged it into shipmaker, you can add weapons, though if you want them to appear depthed you will have to add a placeholder section under the fighter sprite. I acutally recommend leaving some pieces(armor, weapon hardpoints, thrusters) off when you take the screenshot so its easier to add things later and it can be damaged. Since the sprite will be fairly large, I usually shrink it down to .05 since any smaller and you can't even see it ingame. Also want to change the thrusters to 25% thrust length and width.
Thus you get something like this:
Keep the original ship you took the screenshot of though so you can easily edit it if you made mistakes like I did on this one. Its actually 11 sections by the time you add on individual thrusters, armor, and weapon mounts. Good luck with yours!
*edit* In response to what wicky said, ya don't shrink it more than 9 times in either dimension, otherwise its not only invisible, but sometimes I can't get it to appear again!