Eliminating physical cash is not necessary to impose negative interest rates, even quite steep ones. By modifying the exchange rate between physical cash and bank deposits, the economic incentive to hoard physical cash is removed, allowing the central bank to impose an interest rate of their choice while still allowing citizens the flexibility of using their preferred payment methods over short time horizons. This piece[0] produced by the International Monetary Fund delves into the details about the steps banks will take to implement the necessary changes.

[0] http://www.imf.org/external/pubs/ft/wp/2015/wp15224.pdf