It should have this button somewhere, maybe it's labeled under a different name. Check the user manual or the player's settings. It can't be called a DVD player without such a button. Otherwise, the only way to access a specific subtitle is through the DVD menu.
Check the Videowave's functionalities to see if it supports subtitles. If it does not, no worries, just do the transition task. When done, have Videowave outputs as DVD files (IFO, BUP, VOB). Then demux (you can use the freeware PgcDemux for this task) the VOB files as separate video (m2v) and audio elementary streams. Now you need to extract (use PgcDemux) the subtitles from the DVDShrink files and mux them with the Videowave elementary streams again. Use the freeware MuxMan to mux video, audio, subtitles files together.
IFO and BUP files are information files, telling the player how to play the VOB files. BUP is a backup copy of IFO and is used only when the IFO file cannot be read. Without them, you cannot even burn the DVD as Video-DVD, let alone watch them in the DVD player.
Quality won't be as good as the original once you do the transition as the video has to be modified, but you probably won't notice the quality degradation that much so you just have to preview it. It all depends on the settings and how good the encoding/transcoding engine of Videowave.
MPEG-4 is a next-gen of MPEG-1, MPEG-2, and Quicktime technology. Google it and you'll find tons of info.