The ZapMaster (by Thermo) is capable of zapping HBM/MM and then doing a curve trace (ground all pins and sweep a pin positive and negative). There is no time dependence in the curve trace. The only controls I'm aware of is the time delay between zapping and curve tracing.
No the Zapmaster cannot perform V-t capture. but you can DIY - bring a high impedence probe on the zap pin and record it manually on an attenuated input of an Oscilloscope.
Oxy