After reading separate video and audio tracks (in Shotcut), just export a portion of it as one video
I am using Shotcut in version 17.03.02. There are probably more ways how you can accomplish this.

The simplest is to mark in and out points in you video after adding it to the playlist. You can do this using keyboard (I - for in) and (O - for out) also while playing the clip. 

Then you can right click the file name in playlist and either Replace the clip with the new cut points or Insert cut, basically inserting a second clip with the cut points marked. Then you can append the file into the Video Track. Do the same with your audio file. Create cut points and append it to a new audio track. 

You can do some additional trimming in the track editor. For example using the Split At Playhead and delete the parts you don't want. That way you can trim both files to the same length. Now you have to export the project.