a 14 gauge/similar large bore needle "flush" syringe will do the trick. Available in any ER/hospital ward. You can even try asking any paramedic politely and he might even give you one (dont dress like a crackhead lol) and yes its illegal but hey its worth a try. Pop it with the needle, fill the syringe with some epoxy, and fill the area before the glue hardens inside the needle. Go at an angle as to not cause a puncture hole, but rather an "avulsion" type rip. This way, the flap can be closed and will be barely visible to the naked eye.
If you cant get one, email me and ill ship you one.