Remove the needle attached to syringe and cutoff the plastic part from the needle...

Open the cap of lead pen and insert the needle in the cap with the sharp edge pointing outside...

Make sure the needle is visible out of the cap at desired length and glue it using the instant adhesive (or any other glue you have which can hold steel and plastic together)...

Leave the needle in the end cap glued for couple of minutes to make sure it is firmly attached to it and put back the end cap on the lead pencil...

Your scratch pen is ready to scratch the undesired copper from the PCB...