After some research, this is not a package you can just swap out the executable with the standalone Adobe flash viewer (known as the Debug viewer), since this contains within it some other *.dll's written in Delphi and some other random bits that tie the whole thing together (and to boot it's UPX packed).
So, under AppV you'll see this particular package hang on the title screen after the initial animations run. ProcessMonitor just shows it doing nothing after reading some XML file, meaning whatever the cause of the hang, it's occurring in-memory instead of choking on registry or file access.
I got as far as hacking a newer version of Flash#.ocx into the executable (without success--the same problem was present) before I found a slightly newer version that used the Flash9c.ocx instead of Flash8.ocx. Since the entire thing is driven off of XML Files, this worked without issue.
For reference, the copy I used for the new browser was from "Teaching Tutor Reading Mastery Signature Edition Grades 2-5". This particular version had the problem (possibly due to bad media) of missing the file data\_course\RM-R_2-5\RM-R_2-5_course.xml
I was able to look at other Teaching Tutor discs, though, and recreate this manually, pointing to the corresponding files in the XML, changing some paths here and there, and got past this issue.
Some notes as to how to determine if you have an older version of the CD browser:
--Try Universal Extractor to see if you can Un-UPX the executable.
--If this works, crack open the unpacked EXE in a Resource Editor (I used XN Resource editor) and export the RCData resource 'FOCX'. This will be Flash#.ocx, which then you can check the version number of.
--Flash9.ocx was the version I saw worked without issue. Although it seems like it might be possible to hack in a newer version if you use ResHack (since this allows for replacing resources in a PE file).