Um, You're not getting what I'm asking and I get what you're saying about seeking local counsel.
But; If American citizens do take it on, will they be liable for prosecution? Other people have posted lip dubs or parodies/covers, but I doubt they did it to fund-raise. They are not prosecuted.
So, if I do it from my country, and American citizens take it on. Copied project or not; will they be in trouble for it?
Could participants in your fundraising project be in trouble if they publish online themselves lip syncing to copyrighted music? Possibly, yes.
For karaoke, the music is (generally) licensed for use and if you intend to build your entire fundraising campaign on rights-protected material, you will want permission from the holders of these rights.
Disney is not shy about sending cease and desist letters and suing individuals who, without authorization, use their copyrighted material or their trademarks, this whether the use could (in the US) be considered a fair use (or de minimis) or not. And they do not limit suits over infringement to individuals living in the US.
Your first concern should be your own country's IP laws as those are the laws under which YOU will be sued. For a link to these laws, you can visit the World Intellectual Property Organization's website:
http://www.wipo.org
Although I applaud your idea to raise funds to help children, it is recommended that you get proper permissions in place prior to starting your campaign. You might find the holders of rights are more than happy to assist you in your efforts.
Good luck.