You'll want to use a wider BW. The WiFi signal is several MHz wide, so there is very little energy in a 1 kHz bandwidth.
Even though the WiFi signal looks like broadband noise, you could think of it as a narrowband signal that is sweeping up and down in frequency. A wide filter is more likely to capture the signal no matter where it is at any given instant, while a narrow filter (or any given Fourier bin of the same width) will usually miss it completely.
Put another way: yes, you will lower your analyzer's noise floor when you reduce the bandwith, but the time resolution will work against you. The fast-hopping signal will end up spread across multiple bins. If you raise the RBW, the instrument noise floor will be higher, but there will be fewer places for the signal to "hide" at any given instant in time.