I know this topic is 2 months old but I figured I'd supply an easy answer in case someone else comes looking.
First you need to remount the system to be writable:
mount -o remount, rw /
The file you are looking for is located here:
cd /recalbox/system/resources/splash
You can use ffmpeg to strip the audio out:
ffmpeg -i recalboxintro.mp4 -c copy -an recalboxintro-nosound.mp4
Then you can rename the original in case you ever want it back and replace it with the new one with the sound stripped out:
mv recalboxintro.mp4 recalboxintro-orig.mp4
mv recalboxintro-nosound.mp4 recalboxintro.mp4
