You could always present it under the premise of pressure (i.e. just as coal under pressure turns into a diamond, you want to see if you can do it with other objects). This presentation would justify folding the bill very small, and then squeezing it in your closed hand (you could even transition this into coin magic using the same presentation).

I've always used the pretense of showing and teaching the first trick I ever learned as a child. Fold dollar up unfold with one of the moves opposite so George ends up upside down. Then go on with the standard switch routine. Alan mentions it above. Michael Ammar also describes it thus

Instead of worrying about justifying the folding of the bill...just go out and perform the effect. If enough spectators ask why you need to fold the bill into 16ths then you know you better find another trick to perform.