A few points
1. If you had reverse connected the mains lead, the router would still operate in the same direction of rotation. To reverse the motor, you would have had to swap the connections to the brush holders which would reverse the instantaneous magnetic field of the armature relative to the fixed winding (stator or field winding).
2. The cable used appears to be a two conductor cable, so no earth. Standard with double insulated tools, but using hot melt glue to fill the opening where the plug was would not constitute double insulation.
3. You need to make sure that you have physically isolated the hot melt from the brush areas of the machine, as even extremely mild brush arcing is throwing hot conductive carbon particles into the body of the tool. The manufacturer ensures that these particles cannot burn into other components, but they can burn into hot melt and slowly form conductive bridges that transmit electricity either across the hot melt face or to the outside of the machine.
4. If you were to use a silicon compound instead of hot melt as suggested by Mike, you need to be selective about the variety of compound as many are acid based, and could cause corrosion issues inside the machine. The acid based ones tend to smell like vinegar, but some compounds that are acid based don't have the vinegar odour.