I would not have been able to swim that distance at that age, even the shortest estimate. The lake looks like a glacial lake, which would be very deep. Judging by the warnings given round where I live about swimming in chalk quarry lakes, which are similarly deep with steep drops from close to the edge, there could be strong wind driven down currents, as well as very cold water - and here the cold is stressed even in summer, even in relatively small bodies of water. In that large body, that far north and this early in the summer, currents and temperature would be more severe. People were clothed, and this would have made sinking more likely. They were already in shock, and that would affect their temperature control and their ability to swim effectively.
I spent my teens in Dover, where in the harbour was moored a raft reputed to be used for testing paint. It looked close enough to swim to. It wasn't, and people regularly got into trouble trying to. Some really strong swimmers could do it - the head of the local girls' grammar school could, and back - but even the most show-off teeangers knew not to try. The distance to the island looks to be of the same order.

Penny