The HTML Help 2 compiler is available from Microsoft in the Visual Studio 2008 SDK 1.0 download.
(You shouldn't need to have Visual Studio 2008 IDE installed to have these SDK tools.)
Apparently the file needed is hxcomp.exe
After installation of the SDK (on x64 system) the needed file was installed here and the Sandcastle Wizard found it.
C:\Program Files (x86)\Common Files\microsoft shared\Help 2.0 Compiler\hxcomp.exe
On an x86 system it would be found under the regular Program Files
folder name.
Addendum Notes: About tracking down the answer, etc:
According to a CodePlex Sandcastle Help File Builder forum post:
So I checked my installation, and it
appears that I don't have HXCOMP.EXE
installed on my machine anywhere.
According to this article, it's only
in version 1.0 of the VS 2008 SDK. I
have Visual Studio 2008 installed.
-- http://shfb.codeplex.com/discussions/212256
The article referenced in the above post mentions:
Where can I download HxComp.exe?
VS 2010 doesn't use MS Help2 format so there is no Help2
compiler available for it. Starting
with VS 2010, the new MS Help Viewer
format is used
For VS 2008 hxcomp.exe is a part of VS 2008 SDK version 1.0. Note, the
latest version VS 2008 SDK doesn't
contain hxcomp.exe, so you need to
install version 1.0! It is probably
possible to install version 1.0 and
then the latest version over it.
For VS 2005 hxcomp.exe is a part of VS 2005 SDK.
For VS .NET 2003 hxcomp.exe is a part of VSHIK 2003.
For VS .NET 2002 hxcomp.exe is a part of VSHIK 2002 (Visual Studio Help
Integration Kit v2.1).
-- Excerpted from http://www.helixoft.com/vsdocman-faqs/where-can-i-download-hxcompexe.html
Although I found the solution by installing the recommended VS 2008 SDK 1.0, you might use one of the alternate sources listed in the points.