Howdy Ron,
Properly calibrated, the nano should give you much better accuracy than even a very good SWR meter, because a VNA calibrates at many points (101 for the nano) across a frequency span, versus an SWR meter that is calibrated at one point only. And the VNA uses a resistance bridge that is much flatter than the directional coupler used in typical SWR meters. Some things to consider.
1a. You can perform a calibration on the nano thru your existing cables and connectors, e.g., the input cable, the bypassed tuner/meter; and on its output side, PL259 short, open, and load. For the load, use a 100-watt+ dummy load, so you can apply radio TX power and calibrate your cross-needle meter. Then replace the radio with the nano, and calibrate it with the exact same setup. This will give you a calibration through the tuner box and let the nano see what the radio sees.
OR 1b: Cal your cross-needle with a 50-ohm dummy load; Cal your nano at a SMA-SO239 adapter+same dummy load (and PL259 short and open); then move the antenna cable between them; i.e., in both cases the ant coax replaces the dummy load. This will measure antenna without the tuner being in the system.
But also consider:
2. SWR meter indication may rise with increased power, due to all the those bare wires in the tuner (several inches long even in bypass) having some inductive and capacitive coupling within the tuner. On tuner/meter+dummy load, crank the radio's power & frequency up & down. There will be some non-linearity caused both by the directional coupler (probably a Bruene), and some caused by unshielded wires in the tuner. My 3 tuner/meters will vary from about 1.3:1 on 80, 1:1 on 20 (where I calibrate), to 1.7:1 on 10 meters, on a dummy load, and rise a little more with increasing power.
3. Similarly, on antenna, SWR may rise a little with increased power, due to antenna coupling with ground and other conductors in its near-field environment. Set the radio's freq at the antenna's resonance then crank the power up; if increasing power raises the SWR (more than it did with the dummy load), then you know you have some antenna coupling effect (RF induced in nearby conductors causing re-radiation back to antenna, changing its feed-point impedance -- this effect shouldn't increase with power level, but alas, in practice, it sometimes does).
Anyway, my points are that you need to calibrate the nano with the same (as close as possible) setup as the SWR meter uses, and also consider that the power output of the nano is something like 0.1 milliwatt, causing very little coupling effects; versus the 10-1500 watts the radio/amp puts out, causing considerable coupling effects. In addition to all the other possible errors! Like Bruene coupler vs. resistance bridge, grounded meter vs. floating, etc etc.
73, --kv5r