Many species of fish have been tested to see if rapid pH swings are a problem. E.g., fish that evolved and lived in lakes with a pH of 8.5 were dropped directly into water with a pH of 5. Nothing remarkable happened.
Numerous species handle a very wide range of pH (5.0-9.5.) This doesn't mean every species will be as tolerant, but based upon studies I've seen, imo, in the range you described (8.8 to 7.6), it would unusual for a fish to be significantly affected.
Also, although much slower, it's normal in many large ponds for pH to swing up and down every 24 hours (due to photosynthesis and nitrification) along a relatively large range. This doesn't injure the fish or cause them to die.
Naturally this is not recommended for eggs or fry which are much more sensitive, but for adult fish in general it's not a problem.
Also, swings up in pH can be dangerous, not because the pH itself is a problem, and not because pH going up is a problem, but because some metals and chemicals (ammonia in particular), which might be tolerable or sublethal at low pH, can become more dangerous at higher pH levels.
As
duanes
pointed out, high pH water with low alkalinity can suffer from rapid pH declines. Water with good buffers will have more pH stability. It's definitely worth testing your water.