Max9 Those inserted locks are usually fairly soft brass, so you are likely able to drill them open without risking too much injury. That said, power tools near your genitals are always something you need to be very careful about, even if you can align the drill with the lock fairly well.
As for breaking the cage itself, a plastic cage should be breakable with fairly minimal risk of injury by pulling the cage up and holding the ring down. Might take a lot of effort, though, and some superficial scratches are still possible. And as for metal cages, most are designed so compact that, if they have an integrated locking cylinder, you can put your hands on the tail piece, in which case unlocking them without the key gets so easy, you cannot even really call it lockpicking anymore.
