Boat trip from Puerto Natales
The Nandu Discovery Journey is one of the most extensive Patagonia group tours we have, but there is still so much of the area which we can't cover due to its sheer vastness, and navigating the fjords, bays and gulfs is another adventure entirely. However I can see that the Kirke Narrows are indeed within sailing distance of Puerto Natales which in theory makes them accessible in a day trip.
Our Nandu Journey actually arrives into Puerto Natales in the late afternoon after travelling up from Punta Arenas and then leaves quite early in the morning for Torres del Paine National Park, but if you were happy to spend one extra night there and catch up with the group a day later in Torres del Paine, then it's possible you could fit the day trip in. In terms of chartering or contracting a boat and guide to take you to the Narrows, we'd have to investigate the options with our suppliers, with whom we have worked for a number of years and who are always responsive to our requests. One other thing to note is that the navigation rules on the gulf can be quite strict due to weather conditions and the bigger cruise ships moving through the fjords and so chartering a local boat will take some investigation but is not an impossibility.
Perhaps looking at visiting the Kirke Narrows as part of a tailor-made itinerary would allow you more flexibility in terms of how long you would like to spend in the area without having to rush. The area is steeped in nautical history and there are some fascinating stories which have come out of the region – so the opportunity to get to visit somewhere which might also be part of your own history would be a unique experience!