As Sharon says there are skin biopsy tests for certain types of EDS, I think Vascular and possibly Kypho both show up with abnormal collagen formation under a spectron microscope test.
I've had a skin biopsy done, but unfortunately the type of EDS they suspect I have ( a rare form of Type VII with marfanoid changes) doesn't show up under the test. So like most of the EDS types is primarily diagnosed on family and medical history plus symptoms.
It's much the same story for Marfans as their is no definite test for that either. Largely it is diagnosed on meeting certain diagnostic criteria, mainly stature, symptoms, heart and eye problems etc.
It's a very long drawn out and complicated process to diagnose any of the hypermobility or connective tissues disorders unfortunately...I know this one far too well as I'm still in the process of having the extent and structure of my own genetic disorder fully confirmed
In the majority of cases though, hypermobility plus some symptoms is down to hypermobility syndrome (HMS) and it rarely turns out to be one of the more serious and unusual conditions such as the ones mentioned.
Hope that helps.
Love and hugs....Jo