I finally found a solution. The actual error message was that Safari could not load the JVM from
C:\PROGRA~1\Oracle\JAVAFX~1.0\bin\server\jvm.dll (which I assume is really C:\Programme\Oracle\JavaFX Runtime 1.0\etc), a path wihc as I said does not exist on my machine. Using SysInternals' Process Monitor I could see that WebKit was looking up HKLM\SOFTWARE\JavaSoft\Java Plug-in\10.0.1\JavaHome. Now, there are 4 different Java Plug-in entries in the registry, with version numbers 1.6.0_26, 1.7.0, 10.0.0 and 10.0.1; the first three point to a JRE installation but the last one to a JavaFX 2.0 installation. So I removed the highest-numbered entry and after that Safari used the JRE associated with Java Plug-in 10.0.0 and all was well.
It is unclear to me who is the culprit here: there seems to be a bug in Java FX 2.0 but somehow the other browsers (I only checked Opera in detail) are unaffected because they look for other registry keys than this one. The Java control panel makes no mention of JavaFX and designates the JRE 1.6 as the one to use, so it seems to me that WebKit is buggy, too. Oh well.