According to my second favourite book (The Oxford English Dictionary) "waggon" is simply a variant spelling of "wagon." It is a bit more archaic, but there were plenty of cited uses of the form from the 1800s and even one from 1939.
I rather suspect that Tolkien spelled it that way not because it was old and archaic the way that "thees" and "thous" are (that is, nobody uses them anymore), but because it was how the word was spelled in his own childhood in the part of the world he grew up in.
I've got nothing to back this up other than my conviction that the Shire is Sarehole.
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