Yeah it probably would want to be in computers or books, TV......
"crappy Japanese music".... I certainly appreciate you might want the audio of your youth as far as TV shows go but that does seem to be in deference. I am certainly not in a position to debate your choice (it is your choice) and assuming the video they go with is identical (cuts, reedits and such are quick common) is changes nothing as far as technical issues go.
Anyway the tools you want to search for are called muxers and demuxers- there are some heading towards universal ones but realistically you want one for each type of container (to save going into what a container is for now the extension after the video)
As far as I am concerned there are three options for video containers suitable for general use with others being proprietary nonsense the use of which is only justified if you have a technical reason to use it although there is a slim exception for OGM.
1) AVI
Old and knackered but supported everywhere so it sticks around. Unless you have one audio track, video in XVID and do not need soft subtitles in the same file you are good.
The ones below have a single standalone toolkit but there is lots for AVI.
http://www.alexander-noe.com/video/amg/ has a muxer but frankly everything half decent in the video world does starting with http://avidemux.berlios.de/index.html and ending with tools like http://sourceforge.net/projects/megui/
2) MP4
Supports pretty much everything but subtitles (it does have a weird subtitles format/option but I will run away screaming if I have to deal with MP4 time text again).
MP4box is the be all and end all of MP4 until you hit ultra high end professional video that might want some of the extra features to be handled all in one.
http://www.videohelp.com/tools/mp4box although you will probably want to find a GUI for it ( http://www.videohelp.com/tools/My-MP4Box-GUI is the one that still sees updates and I would suggest you go with although I do like YAMB if I need a standalone one).
3) MKV
Supports it all and seen on several standalone players but not as many as MP4 or AVI. Other than the slightly greater lack of support is it can be harder to get things out of it (MKVextract being the tool of choice here) but do try anyway.
http://www.bunkus.org/videotools/mkvtoolnix/ is the tool people use, if they appear not to it is probably a frontend for those tools or the source being ported into the program.
Sometimes you might have to extract the audio first if you have it on another source but several of these tools are good enough to handle it all and spit out the file you want in the end. If you are using something like avidemux generally speaking you load the video, make sure the video is set to "copy source" (or something like it) and then select the audio as an external track.