Technically most of the "terrible rhymes", like the Lehrer ones, are actually perfect rhymes, just a bit unexpected. I never quite understand the custom of making out we don't enjoy those kind of rhymes, when we clearly do.
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Whales and Wales dont rhyme: they make exactly the same sound. That's not a rhyme. Though it would be, I suppose, if your dialect made a distinction between the w and the wh.

If they were the same sound this woudl be an example of an "Identical Rhyme", which is a form which has a long and respectable history, going back at least as far as Chaucer. And Edward Lear goes even further, by using the same word to rhyme with itself in his Limericks. (See entry in A Readers Guide to Literary Terms, Karl Beckson and Arthur Ganz.)

But in fact pronouncing W and Wh differently is surely characteristic of "received pronunciation" in England, with "whale" being pronounced more or less as "hwale"?