Disable calling and texting but not WiFi or NFC

Just check your QuickSettings:

^{QuickSettings (Kitkat / Lollipop; click images for larger variants)}

They will look a bit different on Samsung devices (and newer Android versions), but the basic elements should be there. In the first screenshot, see the last icon in the second row, titled "E-Plus+"? It will have a different title for you (as that's the network provider) or no title at all, but look similar. This icon is for your cellular connection. Tap to turn it off, and you'll have no cellular connection anymore – that means no calls, no SMS, no mobile data. Still, the first icon in the same row (WiFi) will be unaffected by that – so you'll still have WiFi available (and NFC too, of course).¹

Now, when your mentioned "emergency" comes, simply swipe down the notification bar to get to the QuickSettings, and tap that icon again – a few seconds later you should have calls and SMS available again.

Just in case this does not work (e.g. because that icon is missing), take the hint Mord gave: Tap the airplane-mode icon in QuickSettings, and then tap the WiFi icon to switch WiFi back on. Same effect – and for your emergency case, simply deactivate airplane mode again.

¹_{Corresponding icons in the 2nd screenshot (Lollipop): 1st row #3 (labeled "o2 - de+") & #1}