I believe you could just give the two applications different names. Like the name followed by the version number. I could be wrong but it's worth a try.
Not sure if it will work with Handbrake but I run 2 instances of warcraft by having 2 warcraft folders and essentially 2 warcraft.app's.
Click on one it starts, click on the 2nd and IT starts.
So you can probably have handbrakev1 folder, and handbrakev2 folder and you should be able to have 2 versions of handbrake. "copy paste folder" basically.
I did this with Safari when rev 3 came out. I renamed Safari to "Safari2" and then installed the new one and called that "Safari3". They both worked side by side. I think you can do that with any app.