A late reply, but no, that does not really work. Quoting Wiktionary here because I like their usage notes:
"Sensible" describes the reasonable way in which a person may think about things or do things:
- It wouldn't be sensible to start all over again now.
"Sensitive" describes an emotional way in which a person may react to things:
- He has always been a sensitive child.
- I didn’t realize she was so sensitive about her work.
Either is fine, although the former would probably be more likely.