NOTE: this article addresses brush on (bottle kit) touch up paint, not aerosol sprayed paint. 
This challenge is not unique. Especially with super small chips that aren't deep, and where the touch up repair is wider or higher than the surrounding paint. 
Try this before you paint: You can thin the paint with up to 25% distilled water. It will flow better and be thinner in a very small and shallow chip or scratch.
Another trick: try to find a super soft artist paint brush that will allow you to apply less pressure on the paint and clear, so you can put it on even thinner. Sometimes, the stiffer the brush, the more paint you end up applying, because you try to avoid drag marks that the brush leaves. You may also get better results by using one of our fine or super fine micro dabbers to apply even less paint than a brush.
When you try to remove excess paint from the edges of the repair, there are a couple tips in the article below:
We recommend you try using the block method in the article above to provide a completely flat surface to polish with. And you won't need much pressure at all. Another technique that will give you more precise control over removing excess paint, is to use one of our micro dabbers with a little water on it -- this allows you to see the paint you are removing as you do it. Because the paint is waterborne, you can apply pressure with a little water on the dabber to remove the excess. If that doesn't work, then try some polish compound on the dabber. The block method makes it difficult to see what you are polishing away.
Note: Our entire bottle (brush on) paint system is waterborne, so you can easily clean the brushes with warm water after painting the color - that goes for primer, paint and clear coat.
AEROSOL NOTE: For our aerosol paint kits, the paint is waterborne (so it should only be dry sanded), but the clear coat and primer are both solvent borne, so anything used for those steps should be cleaned with paint thinner.

Our polishing compound is less abrasive than most. It is not a "cutting" compound, so it may work better than something you have on hand that is more abrasive. For example, Maguiar's has some very abrasive compounds depending on the particular product you have.
You can see a good comparison of different polish compounds in the link below...our polish compound is in the middle of the range: