Travel from Basel to Lake Como

Yes, an outstanding one from Chur, the Bernina Express to Tirano Italy, then a local train toward Milan on the entire east shore of Lake Como.

Confirming what Sam said. We got off a river cruise in Basel and took a train to Tirano, Italy. We did have to change trains along the route, in St. Moritz I believe. It was a regular Swiss rail ticket, not the Bernina Express company. However, the route was the same the Bernina Express travels. We took a first class ticket and had the car to ourselves for 90% of the trip. Windows opened on the train car so we had a great time hopping from one window to the next to take photos. In Tirano, you exit the Swiss rail building and cross a very short distance to the TrenNord station to continue into Italy. If you haven't already decided, I suggest staying mid-lake on Lake Como. Take the TrenNord train from Tirano to Varenna and stay there, using the ferry system to explore around the lake.

You can look at train schedules for Switzerland at https://www.sbb.ch/en/buying/pages/fahrplan/fahrplan.xhtml
Italian trains after about June 8 will not show up on the schedule now, but the times are 99% not going to change.

Looking at a Wednesday in July, there are direct trains from Basel SBB to Chur at about 11:30, 13:00, 14:30, 16:30, 17:30, 18:30, and it takes 2 hours and 20 minutes. There trains at other times requiring connections. I will assume you are taking the cruise lines flight arrangements to Basel airport. There is a bus from the airport to Basel SBB station about every 15 minutes.

If you arrive early enough to make the 11:30 train, you could make it to Varenna on Lake Como by 20:30, then you could spend 2 nights there before heading back to Basel to get there Friday night to make your Saturday boarding. If later, you could make it as far as Pontresina to spend the night, before going to Varenna first thing the following morning.

One thing you may want to do is store your heavy luggage for your cruise, and take smaller bags like back packs with 2-3 days clothes for the trip to Lake Como. Storage lockers are various sizes up to XXL which may be able to handle 2 large suitcases. You store the bags (so you know they will fit), and then close the locker by tapping your tap-and-go credit card to lock it. Then you have 6 hours of time, but you get charged extra for each additional 6 hours for up to 96 hours total storage time. You open the locker with the QR code on a slip printed at the initial usage, then pay the added amount to open the locker with your credit card. This will make traveling to Lake Como a lot easier than having to drag heavy luggage along.
https://www.sbb.ch/en/travel-information/stations/services-station/lockers/lockers.html

Where are you flying into? If I understand it, you are flying into Basel and want to take the train to lake Como stay for one day and take the train back to Basel to board your cruise ship. The trains I see take 3 1/2 to 4 hours from Basel to Como. That’s a long train ride for one day especially after getting off, and I’m assuming again, an international flight. If you want to see Lake Como why not fly into Milan, Lake Como is only an hour from the airport then take the scenic train to Basel. You would have more time to enjoy Lake Como.

Often I see people take the cruise line's flight booking because it is a good value, and they will route you to Basel.

For someone’s first time in Europe, coming off an international flight and trying to navigate the train system with multiple changes then having to turn around after one day just sounds exhausting and not enjoyable. But that’s my opinion.