If you wanted to edit the HTML files that Rh creates I would say editing them externally is highly likely to give you problems. In the source files Rh is allowed to use PIs (processing instructions) that don't appear in the output but do control how things work. [See UPDATE] Also if you use Rh features, how would you write the code for those? However, you could use Rh to link to those Word files to produce its output. Then whenever you generate the output, it will look at the current version of the Word document and go from there.
I see you are using equations. Do test that they work OK. The trial version is good for one month and is fully functional.
UPDATE - Your external editor would not be able to write these.
See www.grainge.org for RoboHelp and Authoring tips