I don't know anyone who has used small needles on fun fur, but suspect the lashes will get caught in the stitches, not hang loose for that "fur" look.
From experience I can tell you that when knit on larger needles (US size 9 or 10), the chemo cap I made for a friend is very stretchy. It's not warm but it is lightweight and comfortable. (See the "no hair day" pattern at [
headhuggers.org].) Any fancy stitches will be completely lost in the lashes, so knitting every stitch is easiest and fastest.
When using fun fur for the first time, many knitters find it difficult to see the stitches, so often knitters use it together with a strand of some other yarn (as a double strand). This makes a more substantial fabric, but still adds the fun of the fur lashes. The stretch factor is determined more by the second yarn that is added.
Usually knitters seem to pair fun fur with worsted weight yarn, giving a fairly normal fabric weight but with that fur look. What if you paired fun fur with a fine yarn like baby or fingering, and used small needles? I don't know.
Sounds like you're willing to experiment, and want to do things with fun fur I haven't seen done before, so... go for it! And let us know the results. (Partly because we're curious, and partly so we can refer future questions to your posts.)