Not really, that would be känslosamma. Or emotionella.

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.

The stress is wrong but otherwise it's correct.