Use external power - nodemcu 0.9
It looks like the 0.9 uses the SPX3819 regulator. That can run with up to 16V on the input, so 9V on the 5V pin (as long as USB never gets connected) should work fine.

Except: 9V PP3 batteries are useless. If it can even provide enough power to run the board (which is doubtful) it won't last more than a few hours.  You would have to ensure that you use very very deep sleep mode to get any semblence of longevity out of it.

The 3.3V regulator will be throwing away half to two-thirds of the power as heat. So wasteful. You would be better off investing in a 3.3V switch-mode ("buck") regulator circuit (cheap on eBay) to directly power the 3.3V pin of the board instead of 9V into the on-board regulator.