Canasta Going Out with Stock Exhausted and Only One Card in Hand and Discard Pile
No, you cannot.

Whether the stock is exhausted or not, a player with only one card in hand cannot take a discard pile that only has one card in it.

Quoting from multiple rules since with Canasta, like many card games, certain rules can vary depending on the source.

Rule source 1:


  A player with only one card left in his hand may not take the discard pile if there is only one card in it.


And they also clarify that this doesn't change when the stock is exhausted:


  If the last card of the stock is not a red three, play continues as long as each player in turn takes the discard, and he must do so if it matches a meld on his side and the pack is not frozen. (The only exception is that a one-card hand may not take a one-card discard pile).


Rule source 2:


  You may not take the up card if there are no other cards in the discard pile, and you have only one card in your hand.


Rule source 3:


  Taking a discard pile that only contains one card is never allowed if you only have one card in your hand.


If playing Viennese Canasta, you can do this but only if you could legally go out otherwise.


  A player with only one card in his hand may take a one card discard pile under the same conditions which would entitle him to take a discard pile of two or more cards. (Since the player will necessarily have no cards in hand at the end of the turn, this can only be done if the team has a canasta and is therefore entitled to go out.)