DualEyes is standalone, it is also different from PluralEyes - PE synchs sound files with video clips on the timeline of several defined video editors, leaving camera audio intact - DualEyes replaces the video clip audio with the "HD" audio and you can carry on from there with consumer editors.
I don't understand your comment about losing the discs. I've been using these for a couple of years and there was a 30day free trial download and then you pay $99 or $149 for the full product key. If you lost your authorisation, just email Bruce for another copy of the code. Unless you didn't pay.
As far as any alternative app, I think Singular have comprehensively answered the question, how to synch video and audio without timecode. It doesn't always make perfect alignments with the first pass, but persistence and patience is usually rewarded. The last few obstinate ones, I just drag into position and tweak out the phasing.
Good luck and regds,