How to join 2 youtube videos with different ratios (16:9 and 4:3)?
You're either going to have to resample your 4:3 video as 16:9 which will add black bars at the top and bottom, or crop the 16:9 video to fit in 4:3. Either way, the video will need to be re-edited, maybe even re-uploaded. I assume you have editor/owner access to both files?

As far as I can tell there is not way to do this on YouTube via the enhancement section on the Video Manager section. It looks like you will have to re-upload.