Connecting through Zurich Airport

Gee wiz, I think that is close. I assume you are flying Delta because you used points to go Business class. I would see if you could forward your luggage from JFK to Krakow through a separate luggage service. 1 hour 50 minutes would be a comfortable transfer if you did the whole thing on Swiss, but on two different airlines? Yikes!

Does Delta One allow you to bring extra carryon luggage? I just flew Swiss ORD>ZRH, then later ZRH>NCE, then NCE>ORD through ZRH. Swiss was allowing gate checked carryon bags for free because the flights were very full. Avoiding having to collect bags in ZRH is the key to making your flight to Krakow.

Assuming this is in the near future and there are no other flights to Krakow as there are in the late Spring and Summer.

Whoa, you’ve limited yourself to less than two hours. You might want to see if there’s an another flight at a later time to Krakow because the chances of you making that one are extremely slim. And since they’re separate tickets, you do not have the option of Swiss automatically rebooking the missed flight, you will have to pay for another flight and hope there’s seats available.

The absolute best alternative is not to check luggage. There are just too many variables. Late Delta flight, bag delays off the plane, lines at passport, lines to check-in to Krakow, lines at security. I would not say it is impossible, but everything has to line up in your favor.

If you have to check bags, I would suggest leaving on another non-stop flight early the next morning. You won't be in much shape to see much of Krakow on that Sunday anyhow. Good luck.

Do you think we will have enough time to make our second flight?

You may be first off your plane, but how many other planes will have landed just ahead of yours?
I see it as theoretically possible, but unlikely.

Any advice?

Change one of your flights so there is more time between them.

What class seat do you have on the SWISS flight? They have a 8kg limit for carry on. If in biz or 1st you can bring 2 bags, so the suggestion to do carry on only may not be the solution, as Delta allows only one carry on bag.

In my experience it may be possible, but not probable. I would also be concerned about checking the luggage for Swiss Air with such a tight connection. We recently did that with plenty of time between flights, and they still managed to lose our luggage for a day.