Sadly I don't think it is possible to achieve integration without experiencing emotions.
The very definition of integration is to have all experience (including emotion) available to one complete whole. A thinking conscious being without emotion is neither whole, nor integrated.

Emotions are kept at bay for a reason, in DID. The young child who experienced them was completely lacking in the support or the ability to deal with them. Adulthood and therapy gives us the opportunity to reconnect with that part of ourselves in a safe environment. That ain't to say it is easy, though.
Emotions are an integral part of human existence. Unless one is a sociopath, they will be felt and experienced by some part of self.

If not you,
then who?