I don't know of a tester that'll tell you about wiring type. Your best hope may actually be looking at how wires enter the junction boxes, as well as a borescope in any openings therein. Borescopes are quite inexpensive of late and attach to a phone as their power and display. I would use a plastic-bodied one and turn off the power.
What people worry about with K&T is wiring failure. This is easily detected by an arc-fault breaker (AFCI). The AFCI will have trouble if several K&T circuits share a neutral, but that was never a common practice for the same reason it's not today: 2 hots sharing a neutral overloads the neutral unless it's set up just right (MWBC).
There was another worry which was debunked. Consider Romex, run through walls packed with insulation. Despite both conductors packed tight together in an insulating sheath, they don't have any trouble cooling. For some reason, somebody thought Knob-n-Tube would have a problem with that, particularly blown-in insulation done as a retrofit. Further research proved that to be false: insulation-packed K&T didn't have any worse trouble than otherwise. So states have started allowing blown-insulation over K&T.
The third issue with Knob-n-Tube is no ground. NEC 2014 liberalized the rules for retrofitting grounds, so you can add grounds wherever needed.
If it was me and I suspected K&T, I would install AFCI breakers, and retrofit grounds as needed. The cost of a big wiring tear-out is better spent on other safety concerns.