He plays the ignorant, on purpose, of course, making use of 'cyclopedia' as if it were a vehicle.

I think it's a pun, not a malapropism. In my opinion it's also important that he used "walk" and not "go" ... so on foot vs. other means of transportation you can ride on.

[Edited] +6 | -1

There are two meanings here, as in almost all Berra's quotes. The first implication being that Encyclopedia and Cycloped sound alike to Yogi and he could either misinterpret what an encyclopedia really is or could deliberately play on that words..
The sec

The Cycloped was an early horse-drawn locomotive, and the term is now being used a little for man-powered tourist vehicles in various parts of the world. So, is this a Malapropism or a play on words?

To me, Y Berra is playing with the word enCYCLOpedia. Kids, "walk" (not "ride" which would be the easy way) through life and "learn" through your own experiences not a written book.

Sorry, non native comment: "encyclopedia" sounds abstruse (I guess) and reminds a bicycle.

I think he played with the word since it sounds similar to
the name of a "low-powered motorcycle designed to provide economical and relatively safe transport with minimal licensing requirements" (and therefore, appropriate to go to school), ie moped.

I am with the cycloped, because he says "walk" and not "go". This means, they should "go on foot" and not by "bike/vehicle" etc.

I also understood this a Y.B. wanting his children to walk to school, like he used to, i.e. not to go on some "cycloped". This, however, showed up only in one translation out of the four.

I think "walk to school" means "learn such the way".