There is a reason you won't get a size 2 in interchangeable tips, it is that the screw threads for all the other needles which are in the kit would have to be re-engineered. And then the smaller needles are more prone to breaking as well as the screw threads could also bend with the smaller diameter which would ruin them. I have a bamboo set of Knitters Pride and my smallest needles broke, so I replaced the two smaller needles at jimmybeanswool.com but with the metal plated needles.
So if you really need a size 2, you'll have to invest in a circular for this or straights. I don't know of any company which carries size 2 in an interchangeable kit for the reason I described above.
However, you may find that by knitting a bit tighter would give you the right gauge as if you actually had the size 2. You could swatch it up and see if it looks right.
Some designers knit tighter than I do and others knit looser, you may find your needles will work then your headache goes away. Additionally, the difference in width will be hard to see, it is stitch length which will be different. The more time you use the needle not called for will accumulate error. If it is only a few rows, I'd see if it would work. But I would do this outside my project with my yarn in case, I end up having to experiment several times and my project yarn could look yucky. This is why I always buy at least one more skein than the project calls for.