Green’s Dictionary of Slang

imey-wimey n.

[? SE whine or elision of I ... me ... why me? + onomat.]

(US black) a meek-sounding, whining voice.

[US]C. McKay Gingertown 147: ‘I’m in charge of this diner,’ he said in a nervous, imey-wimey voice.
E.B Kelly Points of Departure 121: ‘I’m in charge of this diner,’ he said in a nerve-biting, imey-wimey voice.