Have the Islands of Orkney and Shetland remain Scandinavian until the Napoleonic wars, Norn thus survives until the present day, just like Gaelic in the Outer Hebrides.
Why the Napoleonic Wars? They could easily be Danish (or Norwegian) to the present day. Also, it seems the fact the islands became politically connected to Scotland by inheritance even in the Norse period might've doomed Norn. But looking at how late Norn was still spoken regardless, the islands remaining Scandinavian-ruled for that long means that Norn could at least end up like Manx, if not alive but highly endangered (and no doubt a source of local pride) into the 21st century.