I’m running a 10 speed chainset and chain on a 9 speed cassette.
The difference between the chainsets is that the rings are closer together on a 10 speed chainset. Chain internal width is the same for both, but 10 speed chains have a narrower outer width, I found on mine a 9 speed chain ran fine on the outer ring, but rubbed ever so slightly on the outer adjacent ring when I was riding on the outer cassette rings.
Your 9 speed chainset should run fine with 10 speed everything else, but if you want everything 10 speed, then rosebikes have very good prices on the new 2012 shimano 10 speed stuff.