For a VNA, this is generally not a big issue. The main concern is that the external RF signal should not be strong enough to overload the VNA receiver.
A typical VNA can tolerate a fairly strong interfering signal on the input, and something around -10 to 0 dBm of interference is usually not catastrophic (though the exact limit depends on the particular VNA). So if your local AP is around -40 dBm at the VNA input, I wouldn't expect it to have much effect on the measurement.
For example, I've measured a filter while a 5 W VHF transmitter was operating nearby at 145 MHz on 20-30 cm distance (near field region). It had practically no effect on the measurement results, at most the trace would fluctuate slightly.
The issue is mostly whether the external signal can get into the VNA's (measurement) receiver. If you're using high quality coax with good shielding, a connectorized DUT, and solid connections with a torque wrench, then there's a much smaller chance of a signal entering the VNA measurement receiver. Of course, it helps if the DUT has it's own shielding - the traces, etc. in a DUT can easily pick up strong RF and route back to the device input or output.
A good example of how cable quality is important is the semi-rigid loops on high end VNAs that can be removed to allow direct receiver access. These loops are "exposed" to the ambient RF environment all day, every day, and often in RF "dense" places like labs without causing measurement issues.
And I might be misunderstanding you, but a -40 dBm spur in the measured signal would absolutely wreck quite a few of the VNA measurements I've made. There would also be the risk of that "second signal" creating intermod products within the measurement receiver.
Just my 0.02
