This appears to be the result of two apparently unrelated wellerisms.
I see, said the blind man
Eric Partridge's A Dictionary of Catch Phrases (1986) says:
I see, said the blind man. An elab. and humorous way of saying 'I understand', but implying, of course, that although one understands, one doesn't fully do so—as indeed, the dovetail (which R.S., 1977, remembers hearing as a schoolboy in 1915) when he couldn't see at all, makes clear. B.G.T., 1978, confirms this and adds that it has been esp. common among schoolchildren. In the US, it is much earlier: 'is was common in my parent's speech, and probably in their parents' (J.W.C., 1977): which would take it back to c. 1860. And Ashley, 1983, also from US, supplies the punning 'I see', said the blind man, as he picked up his hammer and saw.
As well as referencing Partridge, Colloquial Language in Ulysses: A Reference Tool by Robert William Dent tells us of the following.
James Joyce's Ulysses (1918-20) contains the line:
I see, says the blind man. Tell us news.
And from Our Mutual Friend (1864-65) by Charles Dickens:
'Let me see, said the blind man. Why the last news is, that I don't mean to marry your brother.'
Forbes Macgregor's Scots Proverbs and Rhymes (1983) contains:
'Sae I see,' said the blin' man.
This phrase is known as a wellerism, which according to Wikipedia are:
named after Sam Weller in Charles Dickens's The Pickwick Papers, make fun of established clichés and proverbs by showing that they are wrong in certain situations, often when taken literally. In this sense, wellerisms that include proverbs are a type of anti-proverb. Typically a Wellerism consists of three parts: a proverb or saying, a speaker, and an often humorously literal explanation.
And includes this example:
"So I see," said the blind carpenter as he picked up his hammer and saw.
Variations on the phrase have been documented in many folklore books, in the USA, Canada, Ireland, UK, Sweden and Finland:
"I see," said the blind man to his deaf wife over the telephone. (USA)
"I see," said the blind man. "You lie," said the dumb man. "Quiet!" said the deaf man. (Canada, 1930s)
Finnish Folklore says:
The wellerism "Niin nakyy, sanoi sokea"("'I see," said the blind man") was common as far back as Renaissance Italy and continues to recur today, often in new forms (e.g., '"I see, sano sokee ja putos jokeen" - "I see," said the blind man, falling into the river"). Wellerisms spread to Finland from Sweden and were especially popular in the 1930s. Some few wellerisms remain popular in Finland today, as in the United States and elsewhere.
As for the wooden leg variation, the California Folklore Society listed at least these three in Western folklore - Volume 18 (1959):
Wellerisms Involving Mention of a Wooden Leg
I see, said the blind man with a shake of his wooden leg, that the price of lumber has gone up.
I see, said the blind man as he peeped through the hole in grandpa's wooden leg (H.42).
I see, said the blind man as he spit through the knothole in his wooden leg
As she waved her wooden leg
Wooden legs appear in other wellerisms, such as this documented in Western folklore, Volumes 24-25 (1965) and the American Folklore Society's (Journal of American folklore, Volume 69)12 (1956):
"Aha!" she cried, as she waved her wooden leg and died. (Idaho)
"Hurrah!" shouted the old maid as she jumped out the window. (Tenn.)
"Hurrah!" shouted the old maid as she waved her wooden leg. (Ky.)
"Hurrah!" as the old maid shouted waving her wooden leg. (Ky.)
Sometimes she would also "roll her eyeballs", or instead of "Aha!" or "Hurrah!" it's "Too late!". In fact, a discussion at mudcat.org lists many variations. These phrases seems to have been used when something has finally happened (playing the winning hand at cards), or something has come too late, or just as an embellished "Aha!" exclamation.
And Lighter wrote:
After reviewing the entire thread, and several giant databases, I feel
certain that McGrath of Harlow had the right idea back in 2006. He
said that the simplest form of the saying was a parody of the final
lines of "Sweet William's Farewell to Black-Eyed Susan," written by
John Gay around 1715:
The boatswain gave the dreadful word, The sails their swelling bosom
spread, No longer must she stay aboard; They kiss'd, she sigh'd, he
hung his head. Her lessening boat unwilling rows to land; 'Adieu!' she
cries; and waved her lily hand.
The form, the scansion, and six of the eight words are identical.
What's more, "leg" pretty much rhymes with "spread" and "head."
"Black-Eyed Susan" was a popular song for 150 years. Captain Whall
even includes it in his book of sea songs and shanties as having been
sung in the 1860s.
The parody words don't seem to be reported until around 1900, but the
large number of variants suggest that it's rather older than that.