I haven't researched this question thoroughly, but there certainly seems to be an instance of "Whee" being used as an interjection to express enjoyment or delight in this untitled item from the Washington [D.C.] Times (November 14, 1900):
The dead silence which followed the President's touching invitation to the members of his Cabinet yesterday to remain with him for another four years is said to have been suddenly broken by a shrill squeal of delight from the foot of the table: "Whee, whee, Mr. President," said the Secretary of the Interior, "I don't know what the other fellows'll do; but I'll stay, thank you, sir." And the Presidential brow remained unclouded, though seven pairs of eyes sought their chief's in silent sympathy.
The president in this anecdote was William McKinley and the Secretary of the Interior was Ethan Hitchcock.
Also, from Wallace Lloyd, Houses of Glass: A Philosophical Romance (1898), describing the end of an impromptu buggy race:
"Keep on, by heavens, and I'll pass you yet," he [Gordon, the loser of the race] shouted defiantly as he made to cross the road behind her. But Miriam foreseeing this possibility still managed to keep directly in front of him, for a few moments, and then held up her hand in token that the race was over and won.
"Whee," shouted Fred. "Better trade your grey off for a yoke of oxen. And we had the heaviest load too."
And from Millard, "The Trolley," in The Youth's Companion (February 8, 1900):
When finally it [a very large U.S. flag on a very tall flag pole] could go no higher, it stopped, and the breeze dying, it pitched head downward, and stood, a strange spectacle of a flag, inverted in the air.
“Whee!” shouted Peter. “What a whirler it is! Beats any kite for ducking!”
And from Arthur McFarlane, "A Return," in Everybody's Magazine (August 1906):
She went down the beach again, and catching on of the lower limbs of the big baswood, proceeded to nip off a hatful of the broad, heart-shaped leaves fior plates. And, “Whee!” she cried, a moment afterward, “I've found a table, too!”