How do I trim OGV files without re-encoding?

Do you really not want to compile yourself? It's pretty easy. Follow the guides here to install the latest version of FFmpeg. It takes a few minutes. You can also download a static build from their download page, which you just have to extract and you're ready to go.

_{I'd really advise you to go for the latest, as the versions shipped with Ubuntu (Mint) are probably buggy and really outdated, and you need a few dependencies when installing with apt-get.}

First of all, you can extract a part without re-encoding anything, e.g. 10 seconds starting from 01:23:

ffmpeg -ss 00:01:23 -i file.ogv -t 00:00:10 -c copy out.ogv

If you want to re-encode the video (which should help in case of synchronization issues), this would be something along the following, for H.264 video and AAC audio (just copy and paste everything, including the backslash):

ffmpeg -ss 00:01:23.450 -i file.ogv -t 00:00:10.000 \
-c:v libx264 -preset slow -c:v aac -strict experimental -b:a 128k out.mp4

For a detailed explanation of what options you can add here, check the x264 encoding guide.