I dont know why Hatsan made the QE like this. They made silencers before.
You dont need a additional silencer, only some adjustments.
Open barrel front , take out the 2 mesh tubes , cut mesh tubes in half and sand the ends. Look for washers 22mm wide , i used washers tar inside for rooftops ,drill holes to 8,5mm. Reassemble the mesh tubes and each time put a washer in between screw end on and finished.
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You can use whatever washer fits , found these with 22mm width and sand them until fit 21,7mm. With belt sander , put drill in hole and let it roll on belt sander.