Rocking Horse with loose handle (Shepton Mallet BA4)

Mamas and Papas rocking horse in great condition except for the handle which has come loose. See photos.

It is useable in its current state but the handle can slide in and out of its socket which is not ideal.

I think needs some head surgery to access the handle fixing point and secure the handle, but there might be less invasive solutions This beyond my upholstery skills, but I'm hopeful there is someone who can give this horse a good home.