I've just ordered one of the chain connectors (s/s with the swivel) - but I'm now wondering whether the swivel might help or hinder the resetting of an anchor after change of wind/tide. FWIW - I'm using a Delta.
Unless the chain is badly twisted it shouldn't make much difference.
An overlooked benefit of an anchor connector is that the pin is usually held in alignment with the slot in the anchor whereas when using a shackle the slot, which is usually much larger than the pin, the sharp edge of the anchor slot may lie on the shackle pin - a high-stress point that could lead to failure. Hylas's suggestion of a toggle looks fine in this respect and I would have bought a toggle had I been able to source one in time.
When you have fitted your new connector, make sure that the connector cannot get locked-up in an inappropriate position in the slot. With my Delta and Kong connector, it would have been possible for the Kong to get caught up; I put a nut, bolt and washers into the Delta slot to make it impossible for that to happen.