Wondering which European currency is safe at this point? Choose carefully.

If you're looking for a European alternative to the euro, some investors are looking north - but these strategists are urging caution.

"As money seeks refuge from the uncertainty in the euro zone, especially with the newly discovered redenomination risk, Denmark has experienced a surge of capital inflows," says Marc Chandler, chief currency strategist at Brown Brothers Harriman. With its triple-A sovereign debt rating, falling budget deficit, and slow but steady growth, the Danish economy looks dramatically better than that of the euro zone, he says.

Strategists at Barclays Capital, meanwhile, say they have "received increased interest in the possibility of the DKK strengthening in light of the euro area problems and would be surprised if interest does not increase further."

But before you go crashing into Copenhagen, consider this: Danish authorities in the past have been more than willing to act unilaterally if it serves their own interest, Chandler says. He adds that it's not inconceivable that they would implement capital controls, as the Swiss have threatened.

The Barclays Capital strategists, in turn, argue that despite the stress in the euro zone, and the pressure on the euro, "we think the Danish authorities will be very keen to keep the peg in order to minimize the kind of economic disruption that the SNB became so concerned about prior to imposing its floor."