I would put a rectifying diode like a 1N400x in series to drop the 0.7V and to prevent the radio from charging the cell.
But more concerning is that the 18650 form factor is larger than a standard AA, so I don't think it will fit.
But the idea is sound: use an AA form factor Li-ion 3.7V cell in place of the dual NiMH AA's. Finding a Li ion AA cell that has more capacity is the challenge I've run into. It would be swell if someone made a dual AA form factor Li ion battery so we can take advantage of the entire battery compartment for the higher power density that Li-ion has to offer. At one point I found a rechargeable camera battery that substituted for two AA's but the capacity wasn't worth it.