as dick_freebird implied, the concern generally isn't what the peak current draw is, but rather what the maximum load step is. Even if your supply is rated to 2.6A, is the load jumps from 0.1 to 2A in a few uS, then your rail will likely droop momentarily and may cause brownout. So you should do transient load testing with a switched dummy load to verify it.
Many scopes, you can use digital persist, which causes traces to leave a ghost behind them which last forever. So set the scope on auto triggering at a fast sample rate, probe current, turn on infinite persist, then leave it alone. You'll see the persist trace of the highest current peak. You just have to make sure the triggering won't miss any short events.