Mine might be a little different than yours - I can't remember how the old handle was made. Mine doesn't have a nut or fastener or anything visible on the bottoms of the 2 hinge pins where the handle swivels back and forth. There is a spring inside the mounting block that holds the handle downward in the detents of the mounting block, and I would think that there are fasteners on the bottom of the hinge pin inside, accessible after the mounting block is removed. Maybe a C-clip. So, I'm not much help and I hope someone will come along and clarify this. If you need to remove a block, I think removing only one would suffice. And the screws are just large wood screws. I wonder if there is a rubberized tape that you could spiral around the handle for a grip.