While I appreciate improvements (disclaimer: I'm not Anna), as far as I know, things pad around floors. I checked that same website for "pat" to make sure I wasn't missing some way that word could be used to describe an animal walking. I am pretty certain cats pad across floors, not pat across them.
Although "padding" is apparently "walking without noise" according to that dictionary I linked, so that might not be the best replacement either considering the sound of the cat walking wakes up the speaker. (I knew the "walking" part but not the "without noise" part until I made this reply.) Then again, https://www.merriam-webster.com/dictionary/pad is more generous to us here, not requiring the walking be without noise, so maybe it does work.
My preference would be "pitter pattering" which isn't as close to the original but fits better with the updated theme. But I think it was a good start anyway.
This meme is certainly not nice... to my eyeballs.
Here's a copy that doesn't force you to strain your eyes just to read it.