1) multimeter min max mode.
2) put current shunt in series and display the signal on the scope
The DMM might not sample fast enough to reliably sample when the transient peaks occur.
A better choice would be to use the scope to probe across the current shunt resistor. Of course, since the scope is not a floating measurement instrument like the DMM, you've got a couple of choices to deal with this.
1) Insert the shunt in series between the circuit and low side of the power supply, and probe across it with the scope.
2) Insert the shunt in series with the positive supply lead to the circuit under test. Probe either side of the resistor with the scope using two channels, one channel on each side of the shunt. Use the scope's math function to display the difference between the two channels.
Or, obtain/borrow a current probe for the scope.