Hey there! Congrats on your Axie baby!
That 5 degree fluctation is just fine. It would be over the course of the day, not up and down like a yo yo, so it would likely mimic what would be natural; the temperature of lakes and rivers get colder when the sun goes down or on especially windy days too! The range is perfectly within what is safe for them too. Your concerns would be rapid shifts in temperature where your 'lotl's body could not adjust and temperatures above 70F.
Water bottles will cause far more issue with more extreme, unstable drops and rises in temp. An air pump WOULD cool it slightly, but only minorly and it would ALWAYS cool it slightly, not regulate your fluctuating temperatures. Depending on the strength of the pump and the type of stone it could actually CAUSE more stress by increasing water current. The reason an air pump will cool a tank slightly is it increases evaporation, which cools the water.
If you REALLY want to cool it, lower the water by a couple inches and remove the lid. You can then direct your fan over the surface to increase evaporation and cool it more without fear of the 'lotl leaving the joint. And I am about to make the WEIRDEST alternative suggestion here; since 68 isnt too warm for a 'lotl (high side of just right), you COULD get a heater and set it to about 66, that way you only ever have a 2 degree slide max. Again, I dont think you actually have a problem you should worry about. Your consistency IS that it fluctuates by 5 degrees. As long as it is consistent, then the axie will adjust.