With only 4% elastane it probably has 'give' rather than out and out stretch. It's not a knit so microtex needles would probably be the best first guess I'd have thought. That's just where the problem is though, isn't it? It's going to be a guess, how low risk is the embroidery that you're applying and, presumably with no spare fabric, what do you do if you're part way through and things don't go well?
I still belong to a couple of machine embroidery groups from when I was looking at buying a machine myself (I decided against it eventually somewhat regretfully) but I seem to see a lot of issues with broken threads and other regular hissy fits.
Nerves of steel required when it's someone else's garment, I suspect!