https://en.wikibooks.org/wiki/Bicycl...ing_Dimensions
The problem is the spacing between the cassette sprockets is different (3.95 vs 4.35).
I have found derailleurs to be somewhat forgiving for shifting, so it may somewhat work, but not optimal.
The easiest thing, however, is to simply buy a 10-speed cassette + 10-speed chain. It should be fine on your freehub.
Your 10-speed shifters should work with most 9-speed derailleurs, as well as 105 & Ultegra 10-speed derailleurs (not 4700 Tiagra 10 speed)