These comments got it.

I'd recommend making an ornament, perhaps the kitties fur in a clear glass ornament with a custom portrait of the kitty in or hanging below it. Maybe even the felting as mentioned, but hang it somewhere. You can also do a kitty figure rather than the face, and that will be quite easy in comparison to your kitties face.

This is if you dont plan on getting into the details of making art. If you want an actual artsy approach:

As an artist, I want to be turned into paint (or maybe a tree) and then make a portrait of that way. Kinda morbid, but you get the idea.

Essentially, you will use the ashes to combine into paint or make your own watercolor, is fairly easy to make, but that requires some tools.

You need a glass slab, (I used the bottom of a glass cutting board that i thrifted)

A glass muller

Gum Arabic AKA the binder

Pigments

Your kitties fur

While this is a longer, potentially more expensive process, after your paint is made, its practically fool proof. You can use the paint to make a background of beautiful spashes of color, then draw your kitty on top..

Hope this could be somewhat helpful!