> So, my problem is, I cannot force HTTrack to evade
> renaming of "~" symbol in downloaded file names.


Yep, this can not be changed currently ; reserved or dangerous characters are
always filtered out not to have troubles on the local filesystem:
<https://code.google.com/p/httrack/source/browse/trunk/src/htsname.c#1267>

I may add some kind of configuration feature for that, but the option might
break on some systems (on Windows, for example)