Is it possible to avoid the use of buffer for finding the critical aggregation concentration (C.A.C) of my tripeptide via fluorescence technique using pyrene as the probe?
What is your plan? Add small amounts of a concentrated pH = 8 protein solution to pH = 8 water? That sounds like it should be ok to me. The CAC will be solute-dependent, but I assume you're aware of that and that's why you want to go buffer-free for this experiment.
Proteins have some buffering capacity themselves, but if both solutions have the same pH I don't see why you would have any issue. You can always verify the pH hasn't changed significantly with small drops on pH strips.
In the absence of buffer pyrene will still show it's change in brightness associated with aggregation. That change is simply dependent on the change in dye environment from solvent exposed in the monomeric state to solvent protected in the aggregate state. It's absolute brightness doesn't matter, you only need to observe a change in brightness dependent on protein concentration.