The former is the third single taken from the iconic rock band's upcoming first album of new material in 13 years, 'Who', and follows the release of 'Ball and Chain' and 'All This Music Must Fade'.
The band's guitarist and chief songwriter, Pete Townshend - who recently described 'I Don't Wanna Get Wise' as "a twist" on their 1965 hit 'My Generation' - said: "I wrote this in a mid-‘70s style, like a song from an album like ‘Who By Numbers’. Warning: don’t get old. You might get wise."
Meanwhile, 'Got Nothing To Prove' and 'Sand' are set to feature on the deluxe edition and triple red, white and blue coloured vinyl edition of 'Who' respectively.
The tracks, recorded in 1966, were "rejected" by the 'Pinball Wizard' hitmakers' then-manager Kit Lambert, and Townshend - who is joined by frontman Roger Daltrey as the only surviving members of The Who - revealed he also offered 'Got Nothing To Prove' to fellow 60s' group Jimmy James and The Vagabonds.
He recalled: "Both these songs are from the Summer of 1966 they would not have been rejected by the band members but rather by my then creative mentor, Who manager Kit Lambert. In 1967, when the song seemed destined for the bottom drawer, I did offer 'Got Nothing To Prove' to Jimmy James and the Vagabonds who used to support us at The Marquee in 1965.
"I remember playing him the demo at my house in Twickenham.
"They were still managed by Peter Meaden who had been so influential on me in particular in the short period he was our PR man in late 1964.
"Jimmy liked the song, and suggested making it more R&B, in a slower tempo, but nothing happened."
Townshend feels that perhaps the song was shelved because he and Roger, who are now 74 and 75 respectively, were too young and not so "self-satisfied" back then.
He continued: "I have a feeling Kit may have felt the song sounded as though it was sung by an older and more self-satisfied man than I was in real life.
"That would have applied to Roger too I suppose.
"Now, it works. Back then, perhaps it didn’t."
The pair got Oasis producer Dave Sardy took work on the recording and 'Blue Planet' composer George Fenton to transform the demo into a "Swinging Sixties" track that is tongue-in-cheek like the fantasy comedy spy movie franchise 'Austin Powers'.
He added: "Dave Sardy and I decided to ask George Fenton to do a “Swinging Sixties” band arrangement to make the song more interesting, but also to place it firmly in an Austin Powers fantasy. I love it."
The track 'Sand' needed some technical work and Townshend eventually “revived" it at his home studio and added some new instruments and vocals which "evoke the era".
He said: "I have always loved it, but have been waiting for computers to get smart enough to fix some of the tape stretch problems that had affected the demo.
"I also revived this in my home studio by doing roughly what I felt the Who would have done had this ever been recorded by them.
"So there is added backing vocals, Rickenbacker, and acoustic 12 string, and a feedback section to properly evoke the era.”
The deluxe CD also features the tracks ‘This Gun Will Misfire’ and Danny & His Ponies’, both of which were recorded by Townshend in the sessions for their follow-up to 2006’s ‘Endless Wire’.
'Who' - which features album art by famous pop artist Sir Peter Blake - is released on December 6.
The Who embark on a UK tour with a full orchestra in Spring 2020, kicking off on March 16 at Manchester Arena, and wrapping at The SSE Arena, Wembley on April 8.