Are the binaries likely to work on a 32bit modern install of ubuntu?
Maybe.
They might require the compat-libc5 library packages, and you may have to manually install /lib/ld-linux.so.1 before they are recognized as "executables". Or not. Try them.
Should I just virtualize the current redhat machine and put it behind a (hopefully password protected) proxy?
Yes, absolutely virtualize it (the whole bundle.. just copy the hard disk). Then use the host machine security to protect them.
Cheers