Here are results of testing with _inmm.dll. I have no prior experience with this tool so I don't know if I did something wrong, which is why I'm posting the whole thing here.
To cut a long story short, it doesn't work because the game doesn't import from WINMM.DLL. I suspect the game is using its own functions (probably from WINPLAY.DLL in the game directory) to play the CD audio.
Here's how I tested:
Downloaded _inmm238.zip from http://www.geocities.co.jp/Playtown-Domino/8282/
Copied _inmm.dll to c:\windows\system32
Extracted the other files to c:\games\inmm
(I used the ZIP rather than the auto-installer as I like to know what files are going where)
Created a new string value "InstallPath" populated with c:\games\deathtrap under
HKEY_LOCAL_MACHINE\SOFTWARE\Eidos Interactive\Deathtrap Dungeon
in the registry.
Added the following to _inmmcnf.ini:
[Deathtrap Dungeon]
Group=EIDOS Interactive
RegKey=HKEY_LOCAL_MACHINE\SOFTWARE\Eidos Interactive\Deathtrap Dungeon
Value=InstallPath
File=DUNGEON.DLL
Message=My Deathtrap Dungeon
Ripped the CD audio as MP3s to c:\games\deathtrap\cdaudio
Files are named "01 Track 1.mp3" ... "15 Track 15.mp3"
Ran _inmmcnf.exe
On _inmm.ini tab, clicked Add and selected the 15 tracks
Saved changes to c:\games\inmm\inmm.ini
Went to Patch tab and selected EIDOS Interactive and Deathtrap Dungeon (that I'd added to the _inmmcnf.ini)
Clicked on the patch button.
Despite my new registry key it said "Information not found" and prompted for the directory where Deathtrap Dungeon is installed, so I manually selected it.
It correctly picked up DUNGEON.DLL as the target file though.
I pressed OK but it said DUNGEON.DLL: no imports from WINMM.DLL.
Looked in the game directory and found WINPLAY.DLL and WINSDEC.DLL
Tried those also but again no imports from WINMM.DLL