Hi There! My name is James and hopefully I can help.
I know that you can mute the audio within the mixer, but I am unsure if you can record
only the video. If you had 0 audio sources in your source window, then no audio will be recorded - however, there still may be an empty audio track when you put the recorded file in your editing software. However, I know in Adobe Premiere Pro you can drag just the video clip onto the timeline (I.E you wouldn't have to delete the audio from the timeline every time).
Here's a quick video I found on how to do that in Adobe Premiere:
https://www.youtube.com/watch?v=0r5BJsx2vSY
However, if having the audio track truly is a problem for whatever project you might be doing - you may be able to disable it in "Audio Settings" and/or in the "Output Settings." Or another alternative is to run your recorded file through Adobe's Media Encoder (which should be covered by your Premiere license). From there you can select a video format before you were to put it into Premiere.
I hope this helps! Please let me know if there is anything else I can do. If I find a solution to completely negate the audio directly within OBS I will post it below in this thread.
Happy recording!