The short story - you may be warned and you know in all it's a heavy task to migrate your VB6 app maybe without reaching a simple way for migrating WinHelp to HTMLHelp.
The official recommendation (10 years old):
Forget about WinHelp, it's history and migrate to CHM help file format.
But, maybe you already have found my answer (search for Run WinHelp on Windows10) and read all further links:
Please note a tool called HHPMod especially for migrating context-sensitive F1 help.
I tried the WinHelp of an old VB6 program before and after the fix from above and it is working for me on Windows 10 (Version 1803).

Another solution you may want to try (depends on your deploy and IT environment):
Quoted from this article (thanks to Komeil Bahmanpour):
"Please note users who have tried to replace winhlp32.exe manually in Windows folder and winhlp32.exe.mui in Windows\en-US folder of Windows 7, was faced with overwrite restrictions due to ownership and permission problems."
Additional information:
I may well be wrong, but I believe that also (old) online help files are usually copyrighted as part of Microsoft Windows. Distributing the files would normally constitute a violation of copyright law (as you mentioned in your question).
AFAIK developers are not allowed to distribute the Vista version of WinHlp32.exe or included it in their installations. Every individual user who wants to use WinHelp must download the WinHelp update directly from Microsoft and install it themselves.
Help for applications has been .chm for many many years now. Microsoft released the tool HH Workshop (HTMLHelp SDK 1.4) around 1997. Around March 2006 during discussions with MVPs, Microsoft Help team announced that WinHelp would be deprecated (phased out). WinHelp is architected in such a way that Microsoft would have to rewrite it from the ground up to meet the Windows Vista code standards. Since then .CHM has been the only choice for our application help.
What does this mean (please note we are about ten years later now!):
- WinHelp runtime (WinHelp32.exe) no longer ships with Windows Vista/7/8/10
- ISVs (Independant Software Vendors) should stop promoting WinHelp as a viable help system.
- Help authors should move over to HTML Help 1.x (.chm) if they haven't done so already.
HH Workshop is sufficient to author .CHM help files. I'm using a tool with a few more features (drag and drop TOC/Index editing etc) called "FAR HTML". Then there are high-end more expensive tools (you mentioned RoboHelp) that have advanced features such as "convert between different help systems".