How to calculate sine wave SNR from oscilloscope
For all the reasons above, an oscilloscope is inadequate to this task.  Here's a couple of alternatives:
Method 1: find someone with a really good spectrum analyzer, and borrow time on it.
Method 2: build a really good notch filter (for a one-off you'll want to use analog components, and good ones).  Characterize it (I didn't say this would be easy).  Then run your 1kHz signal through the notch and look at the remainder in the O-scope.  Once you get rid of the 1kHz tone, whatever remains is the stuff you don't want -- characterize that, add the 1kHz tone back in on paper, and you've characterized the net effect of your DAC and your notch filter.
Note that method 2 requires some significant analog chops.  If your go-to solution involves white proto-board, junkbox capacitors and LM741 amps, you probably need to up your game.