playing defense against an unhappy copyright owner and we don't think you want to be in that position.
Cutting it out. As a general rule you should assume that if you're cutting out and animating a copyrighted image, then you're infringing. Whether you get hassled depends on whether the copyright owner finds out and cares enough to hire an attorney or write a letter. If you're seriously risk-averse, Bob the Builder and some versions of Alice in Wonderland are protected under copyright laws, so you would stay away from these. Although some Charlie Chaplin films are in the public domain, the use of Charlie's image for a commercial enterprise may trigger right of publicity laws (yes, his estate has an agent). Normally, academic uses like yours might remain undetected but with the unlimited spread of MOOCs, you never know who will see what.