Further to this, I built batik-1.9 from source using JDK9 and got the same issue.
Investigating, this is due to:
Class org.w3c.dom.Window is defined in batik-ext.jar. Other classes in the org.w3c.dom package (e.g. Node) are provided by the runtime (running with -verbose says it's from jrt:/java.xml) but Window isn't. My conjecture is that this prevents the classloader from looking any further into jars specified by the application, and maybe this has changed between JDK8 and 9.
I then renamed the package in the source for batik-ext.jar and fixed up all the references in the rest of batik. Obviously this is only a hack.
Then I found that I could start squiggle and open an SVG file. I don't know if this caused any other issues elsewhere.