Firstly you are using the op amp in such a simple configuration, that most of the characteristics of the op amp will not matter. Your gain (in the config in your circuit) is 1 + Rf/RI where Rf = Ri = 10k, so your gain is 2 (pretty much regardless of the op amp's internal characteristics). The 100dB gain is the internal gain of the amp, but you are reducing the overall gain (to 2) using external feedback resistors, so this characteristic of the op amp does not matter
In your configuration, the only parameter that will affect the performance of your circuit is the input offset voltage (this will add/subtract a dc voltage to the one your are measuring implying a temperature error) and the part you have chosen is better than the part they have suggested.
Both parts appear to be stable at a gain of 2
Your CMRR (the ability of the amp to reject signals that are common to both inputs) is not important. The PSRR (the amps ability to reject noise on the power supply) is not important. Slew rate (how quickly the output can change) is not important (temperature does not change in microseconds).
I see no reason why you cannot drop in your suggested replacement.
Hope this helps