I'm not familiar with the verse, but here are the chords I use:

(G) Button up your overcoat (G#),
(A) When the wind is (A7) free
(Am7) Take (D7) good (Am7) care of your(D7)self
You be(G)long to me (D7)

(G) Eat an apple every day(G#),
(A) get to bed by (A7) three
(Am7) Take (D7) good (Am7) care of your(D7)self
You be(G)long to me (G7)

Be careful (C) crossing streets Oo – oo!
(G) Don't eat meat Oo – oo!
(Em7) Cut out sweets (A7) Oo – oo!
(D) You'll get a pain and (D7) ruin your tummy

(G) Keep away from bootleg hooch,(G#)
(A) When you're on a (A7) spree
(Am7) Take (D7) good (Am7) care of your(D7)self
You be(G)long to me.

You could simplify it by leaving out the G#, staying on D7 where the Am7 is indicated and playing an Em in place of Em7.