Your 2 major choices are write an AX object to call it, or an NPAPI plugin to do it ... as others have said, that creates a gaping security hole, so engineer the plugin/ax to ONLY call the known exe - I'd CRC check it too if I were you
You mention it's written in delphi - you may be lucky, delphi creates IDispatch objects left, right and centre - have a look at the exe with
oleview.exe
- you may find something in there you can directly invoke via script (in IE only) via
ActiveXObject[
^]