You cannot disallow the share button. That's a site feature on every open blog. You would have to set your Spark Page to private (friends only) and just hope your friends don't share.
Why do you want to publicly blog but disallow sharing? You don't want people sharing your wonderful inspiration with others?
As Heather said, anything you can see online can be shared, regardless of buttons to do that with - you just copy the web address. So hide it if you don't want it shared, or as you said, just don't blog.
BTW, if you go My Trackers - Planner - Journal that is a 'blog' that is private to you and you alone. Nobody else can see that one. That might be where you want to put your thoughts if you desire privacy.
Deb, in New Zealand