The sense wires are only needed if the leads between the load cell and ADC/microprocessor are long, as they allow the micro to account for the voltage drop in the current-carrying excitation wires.
Unethical not to consider it I think, even if it is as small a quantity as a fraction of a gram.
Is there no ability to calibrate it? A special 25g weight kept in a glass case and only handled with white gloves once per season?
If your application is that important, you should be getting advice from an industrial weigh scale consultant, not a hobby forum.
It's not uncommon to put a NTC type thermistor onto the strain gauge and use a second channel of the strain gauge instrument to measure temperature.
The resistances between the wire-pairs are as in the attached file "ohmPairTable.png", deduced using a digital multimeter.