You don't need to apply for stinky-winky NRN card. As long as you don't go around being a pretentious prick by flashing your passport, you can continue enjoying all the benefits as an 'authentic' Nepali citizen by using your Nepali citizenship.

The new constitution has a provision that allows you to apply for 'new' one meant for non-resident Nepalis. By using the new citizenship, you can enjoy all the rights as a Nepali citizen except be involved in Nepali politics. The catch - you'll need to give up on your old one. By law, you're supposed to abandon your original Nepali citizenship right after you've acquired a foreign country's citizenship. I'm yet to meet someone that's submitted their Nepali citizenship, though.