My GF didn't have a clue until I came out to her. My sister thought I was gay before I told her the truth... most of the people don't even know that CDing exists as a habit that is not dangerous or harmful... it's a taboo, therefore most people never expect it from someone close to them.
Regarding the clothes and shopping and stuff like that, women just think that you're a good partnerNow, when it comes to having your own stuff in your house, then you should tell your SO about your CDing. Otherwise, having such stash wouldn't have any reasonable explanation, and believe me, most of the times, the people won't be thinking that you like looking like a girl :P