A very minor point but Google suggests that it has not been hitherto noted.

On browsing some Kipling recently I noted that there is a Just So story called "The Cat that Walked by Himself." I submit that this is the obvious inspiration for the title of TCWWTW.

Peter, you naughty boy! I didn't know you kippled!

(Enough Mauve Decade jokes for one night...)

I don't know if this will be helpful, but --

The original title of the book was The World Snake, but the editors didn't like a title with "snake" in it. So it became "The Reluctant Knight" (Heinlein typed the new title on a 3x4" label and pasted it over the title page; over the years the gum dried up and the label fell off). At some point Ginny suggested "He Walks Through Walls." Heinlein said something like "That's not quite right, but you've got something there" and came up with the title. Ginny's only objection was that Pixel not being a human, it should be the Cat That Walks. Nonsense, R said.

Given that the title came from Ginny, it might well have a remote root in the Kipling story title -- though, as Eric points out, there is no resemblance of the stories. And though Heinlein was less a fan of Kipling's stories than of his poetry, it's entirely possible that his reworking of the title was equally inspired by the Kipling title.

I rate this a good conjecture.