Are there any video programs to trim and export multiple videos at once?
If all you're doing is trimming the video, you may want to consider the command line tool ffmpeg. 

The -ss flag will allow you to set the in point for your trim. You can also set an out point on with the -t flag.

For example, the following command will take "name_of_movie.mp4", trim the first 10 seconds off, copy the audio and video codecs, and output the file as "name_of_movie_trimmed.mp4"

ffmpeg -i name_of_movie.mp4 -vcodec copy -acodec copy -ss 00:00:10 name_of_movie_trimmed.mp4


This should work for any format that ffmpeg accepts, which is pretty much all of them. If you'd like to script it, here's a starting point that I use for this very purpose. Edit the extensions for the type of file you use, and for the time you want, put it in a directory with the files you want to trim, and let it get to work.

#!/bin/bash
for file in *.mp4; do
name=${file%%[.]*};
ffmpeg -i "$file" -vcodec copy -acodec copy -ss 00:00:10 "$name trimmed.mp4"
done


There's a lot you can do with ffmpeg to automate some of the more tedious parts of working with video, so have a look around!