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You can use a hand drill , just be careful. One slip and you got more holes or scratches to fill. I used a hand drill a couple of times in the beginning and you need a good center punch to start it....

I would take it apart and clean up those scales. A little fine sanding and polishing and they may get clear. As for the wedge ,,,, it looks like maybe the pin is just loose. If you did want a wedge...

It has honey horn scales that appear to be made wedge less. Not a bad razor it just looks like it has lost some of it's character over time. I will let others take a stab at date and maker.