Just letting people know I've solved the issue and got both games to run.
As stated before, I got the download versions of both games which don't have a single installer exe, but rather a zip-file with all the game files that you extract into a folder and then start without further installation-stuff. Also included in both zips was a whole slew of DirectX-related files...a DXSetup file, a DXMedia file and a bunch of DX-related DLL-files. Anyway, I moved all those files to a different folder, leaving only the game's exe-files, the game's data-files (with an ARC-extension) and the documentation files in the game folder and suddenly the game stopped doing the "can't initialize DirectSound"-thing and executed as it should. (only to choke on Snow Drop's brand.avi file, but if you remove that file too, the game complains with an error but still proceeds to intro and main menu afterwards...I can live with that)
To Jast...I do kinda wonder, is there a particular reason for distributing these two games in a normal zip, rather than an installer and is there a reason for including all those old DirectX-files, which the game apparantly tries to adress as long as they're in the same folder even though those dll-files are really outdated? I believe they're all DirectX 6-files, so it's unlikely anyone's gonna install them...you might just want to leave them out.