Can I safely replace rechargable NiMH batteries with consumer-grade ones?
1) Yes, since the newer cells are of a quality brand and have the same or higher capacity than the old ones, and the nominal voltage is the same. I'd say that's "safe enough". (Take it from a random person on the Internet.)

2) Possibly. Is there a temperature sensor in the circuit somewhere? Holding the cells tightly together with sticky tape or cable ties, and squeezing some hot glue into the gap between them should do the job without thermally insulating the cells too much from the surroundings.