Electrical – Will this non Contact voltage detector be adequate for the use case

You are required to use whatever type of wiring your local code permits for this type of connection. If you are in a residential location then it is likely NMD90; if you are in a commercial location then it will likely require BX/AC. The shielding you are referring to between the can and the box isn't really BX/AC; its just flexible metal conduit. It looks similar to BX but it's not the same thing.

If you do use BX/AC, make sure to use plastic bushings at both ends of the cable so you don't nick the conductors with the sharp BX/AC.

Usually with cans, there is a friction cable clamp you just push the NMD90 through, however if you use BX/AC then you will need to use one of the punch-outs and a proper cable clamp to secure the cable.

The following should be sufficient to determine that it's safe to work inside a switch box.

• With the breaker(s) for this box turned on, touch the NCVT to the wallplate or insert it into the "hot" (narrower) blade socket of the electrical outlet you'll be working with. The NCVT should indicate live wiring. This is primarily a test of the tester itself; it should light on a known hot circuit.
• Turn the breaker(s) that provide power to this box off.
• Return to the box and repeat the test; the NCVT should not indicate live wires. If it does, you flipped the wrong breaker or didn't flip enough breakers to make the entire box "cold".
• Open the wallplate, and touch the NCVT to all screw terminals on all devices in the box. The indicator should not light; if it does, you missed breakers (or there's a more serious wiring problem like shared neutrals).

At this point, I'd be confident of not getting hurt working on the box. If you REALLY wanted to be sure, you could take a multimeter and test the AC voltage between all terminals on each individual device; all readings should be zero. This may be necessary if you suspect a voltage leak (faulty breaker, miswiring joining unrelated branch circuits together); an NCVT requires 50VAC to indicate "live", but 45V can still give you a jolt with sweaty/wet hands (remember that a car battery, only 12VDC, is an effective instrument of torture).