The Swedish colony is Delaware during the 18th century included a lot of Finns (perhaps most of the colonists), and is the Finns that are usually credited with introducing the log cabin, the Scandinavian form of house, to the Americas. The Finns are a woodsy people by European standards and reputedly have the same sort of disruptive qualities that the Scotch-Irish have, so it made sense for the Swedes (who owned Finland at the time) to use Finish settlers - they were best suited to the New World and they would be far away from the Swedes.
Faragher's biography of Daniel Boone claims that the descendants of the Finns were still still a distinct group, active as woodrunners and friendly with the local Delaware, in the 18th century and taught a young Boone his skills, but I have never been able to find documentation to support that.
It seems likely that the Finns would have brought their pukkos with them, but 1) said pukkos may not have been the same as the modern version - I know the basic shape has been around since the pre-viking period but I wouldn't assume that a 17th century pukko was identical to a modern variant without seeing an original example and 2) any knives they brought with them would have been relatively few in numbers and used up well before 1700 or so.The chances of one surviving to be used after that date are nil, in my estimation.
Apart from New Sweden, I know of no significant immigration from Scandinavia to the Americas prior the mid 19th century.