The wheelbase of the 737-500 is 11.1 m through to the 737-900 which is 16.97m, so they all fit under the 18m limit. So the 15m minimum width applies for the taxiway. I checked the FAA and they are also 15m width for the Boeing 737 (FAA design group III, ICAO design code C). The Australians permit a reduction to 15m width for less than 18m wheelbase.
In the back of my mind, I have the thought that you can get it into narrower taxiways by applying the UK CAP168 or FAA minimum clearance between "the edge of the taxiway and the wheels". Then you can get down to 12.1 metres width, but most authorities will round that up and state their required minimum width. Might be able to get a dispensation for a one-off or if the aircraft is marshalled or switched off and tugged.