The pattern uses size 6 for sport weight, which isn't that much heavier than fingering and does say any sockweight yarn should work. Try 4s and 5s to see how close to gauge you get and if it's dense enough for you. Everyone knits with a different tension so it's hard to say if you really do need to go down or not. If you knit tight, 6s may work fine, if you knit loose, maybe the 4s. If your gauge is smaller on the smaller needles, you can make the larger size for length and knit rows until it fits you.
sue- knitting heretic