You'll never feel comfortable with conflict without engaging in it. Try desensitizing yourself systematically. Start out by having a small conflict with someone who overcharges you in a restaurant - someone who you probably won't ever see again. Move up step by step to prove to yourself that you can handle conflict. No one will end up dead, and you can even talk with the person you've challenged afterwards.
Procrastination has a lot to do with shame.
Your shame will either come from not being able to face the challenge, or from somehow having your expert status in the organization compromised because you failed to deliver. Procrastinators do finally get the work done, because a deadline looms or the shame of not completing the project outweighs the shame of their work not being good enough. Whatever procrastinators do, they feel that it's not good enough. They envision themselves at the top of the mountain, but they don't want to learn how to climb. They imagine that everybody is watching them learn how to climb a hill.