HTML Help Workshop is pretty old software, so it sometimes has trouble configuring itself in current versions of Windows. After installing it, you should see a menu option File->Publish->For HTML Help in Arbortext Styler. If that option is disabled, it means Arbortext can't "see" your Help Workshop installation.
To fix it, you can force the association of *.hhp files with Help Workshop:
Create an empty file called "dummy.hhp"
In Windows Explorer, double click the file. You should get a prompt from Windows about which program you want to use to open it. Select the "More programs" option, and navigate to C:\Program Files (x86)\HTML Help Workshop, and select "hhw.exe". Make sure the "Always use this program" option is selected.
If Arbortext Styler is open, close it and reopen it. You should now see the HTML Help publishing option available.