Just saw “The Cow Says: Moo” video. That sounds like a vinyl record rather than a digitized recording.
For that you want a narrow band equalization (200-4000Hz ish ), and some “needle on record” noise, e.g. here ,
or here … Freesound - 15-seconds-vinyl-noise.flac by notKlaatu
You may need to speed up the “needle on record” sample: the disc in the toy would be spinning faster than a 45rpm.
You can get two free warping effects for audacity here: namely “turntable warping” and “Random Pitch Modulation”.