Copyright law is confusing. Whistling a popular tune can be a copyright infringement, if a rights-holder decides to enforce it.
When uploading a recording you can be, but are mostly not, at risk of serious consequences. But as a law abiding citizen one wants to be sure that uploading you Ukulele clip, does not cause you any harm. Just remember: Louis Cole does not care about or is offended by your dub.
Sure you can! Right now you can give me encouragement or suggestions by telling me. For now I will keep on doing my thing and playing my drum.
If enough people support the idea, we can get make this jam a reality.