Check into whether iMovie or Pinnacle video editing apps let you export audio only. Video editors in Mac and windows typically have this ability, so it's possible one of these iOS apps can do so.
If either do, there's a chance you won't have mp3 as a format option, but rather something like AAC or AIFF. These are in my opinion better codecs, but may not be supported if you're sending the file to someone on an old PC.