Step 2 : Sing it!
Rhythm and contour (the up and down shape) are the two most important factors in tune-recognition. The right notes are surprisingly less important.
If you stick to your prepared rhythm and follow the approximate shape of the tune up and down, a crazy vocal shot will give you a surprisingly good sense of 'how it goes'. When you come to play the right notes on your instrument, you'll find that you're playing something that is strangely familiar.
Play the scale and the starting note, then have a go . . .