Looking at some uninstall instructions for ProTools, the DUI.shlib is Digidesign specific.
0x1222000 - 0x127fffb DUI.shlb PEF binary: DUI.shlb
It's not uncommon to use shlib as a file extension. GCC (part of the developer tools in OS X) uses it as well.
Although the binary in the file is a PEF, it may only be compiled like that and used by carbon to load it as you noted the rest of the app is carbon.
The thing is PEF or not, it may use OS X specific libraries that are not available in OS 9. This wasn't uncommon in carbon apps. They maybe carbon but use external libraries.
0x1222000 - 0x127fffb DUI.shlb PEF binary: DUI.shlb
The last part (: DUI.shlib) is an export name for the library for the linker to use.
The output is a list of libraries loaded by the Carbon Code Fragment loader.
So really it comes down to what libraries DUI.shlib imports and if they are available on OS 9.
If you want to send me a copy of that file, I can look and tell you what all libraries it imports.
In theory it may be possible, but I wouldn't count on it, though stranger things have happened.