Replacing jpg/png to webp and keeping compatibility

To your last question, I think the answer will be no (about cf), but you can still do what you want without it.

1) First, cf does not currently support webp format in its various image processing tags/functions, so it can't be used to do that conversion. But of course many other tools can do that for you.

2) Second, as for changing the incoming requests from png or jpg to webp (once the images are converted), note that cf would never see those requests (as such static files are handled by your web server, like iis or apache).

But that's where you COULD change your image requests from one file extension to another, using a url rewrite. Too much to elaborate on here, and the steps are unique to each web server. And there are also reasons it may not work well for you, as a solution to this problem you present. 

Of course, you could just do a global find and replace in a decent editor, to change the image file extension references in your cfml. Just be sure to do a backup of your code before such a major change, in case you want to revert.

Others may have better ideas. I just wanted to start with some. 

(Also, beware to change a SAMPLE page first, to see if this suggested change to webp really solves the problem. It may not, in which case you'd not want to bother.)

3) There are indeed many other possible ways to speed up a site, again many having nothing to do with CF, so you may find still other solutions to consider, in your research.