We have a series of projects that have SWF Animations. Is there an easy way to convert the SWF Animations to something HTML5 compliant?
No easy way, sorry. Depending on the type of animation, maybe you can replace it by Effects on object(s). If more complicated, you can create a HTML animation (OAM) to replace it, or an animated GIF.
If they do not not have much interactivity or ActionScript, you should be able to export them from AnimateCC and zip that output and import to Captivate as HTML5 animations. I can get tricky bit is possible depending if there is script, they also need to be AS3.