\setuphead[subsection][style=cap]  %aborts compilation. (But
"slanted" works)

I also unsuccessfully tried "style=\cap" (or \kap etc.), "command=
\cap" etc.  (But style=\sc works. I don't want small caps, though).


Did you try \WORD{} ?
see http://wiki.contextgarden.net/Basic_Text_Formatting

AFAIK \cap and \kap are LaTeX...

Greetlings, Hraban