What you want is known as a Gray code for integer partitions. 

It exists.  

See C. D. Savage, Gray code sequences of partitions, <i>Journal of Algorithms</i> 10 (1989) 577-595.  Disclaimer: I haven't actually read this paper.  Other sources such as <a href="http://www4.ncsu.edu/~savage/AVAILABLE_FOR_MAILING/survey.ps">this 1997 survey by Savage</a> and <a href="http://www.cs.uiowa.edu/~sriram/196/fall01/lecture7.ps">these class notes</a> don't say what the construction is but say that it's complicated.