I am moving out of rental, and there are some nail holes in the wall. I don't want to use spackle, because it would require me to repaint the walls, and I don't want that.
What is an alternate solution to hide the holes?
If your goal is to fill in the hole with a color that matches the paint, without having to actually use any paint. then your best solution is probably going to be either using a bar of soap, or wax from a candle.
As long as you can get the color of the soap or wax to match the color of the wall, no one should be able to tell that it's there unless they happen to touch it.
What you would do is take the bar of soap or wax that matches the color of the wall, and for the soap you can just rub the it around the nail hole to fill it with the shavings, or like with the wax just take a knife and cut a piece to press into the hole.
Both the soap shavings and wax should be malleable enough to shape if you have a textured wall. Allowing you to hide it even more.
If you're having trouble finding soap that matches the right color, you can look for a place that sells homemade or organic soap. They will usually create different colored soaps than the typical white or blue soaps in convenience stores. If you're feeling really crafty, you can melt soap and mix in colors yourself. If you're really adamant about using this method, you can create your own soap.
Wax is easier to find. just buy a cheap candle. But typically you're only going to find white candles if you're looking for the cheap/small ones. Luckily, it's really easy to melt wax and add some food coloring to it in order to get the desired color that you want.