Do I need to install a fuse on a altenator wire?

That can be dangerous AJ, get the header wrapped around the drive shaft
Never seen that happen, and cant imagine it, but.............. never say never I guess. Headers rattling on stuff used to be common in our A-bodies; there is only so much room under there, and it all wants to occupy the same real-estate when it goes past the bellhousing. I've even jammed a chunk of 2x4 in there in a temporary pinch.
Another thing a strap like that can be used for is to support the exhaust after you unbolt it from the collector.