Right, but I think the thickness of the crystal should be related to the order of the pulse width! Also, why is called single shot? I think it still need the scanning to look for the fringes and all the autocorrelation parameters!
Regarding autocorrelation, you could think about several setups, and that, of course will affect the crystal requirements. Some of the more convenient ones are well described by R. Trebino, just Google for swamp optics company.
Michelson interferometer will give you all the information about spectral content of your pulse, by absolutely nothing about the temporal characteristics.
I think the main difference between them is with or without a delay unit. For regular autocorrelation (either intensity autocorrelation or field autocorrelation), you need a delay stage to scan through the whole pulse in order to get one autorrelation trace.
For single-shot autocorrelation however, you focus the two beams on the crystal in only one dimension(with cylindrical lens for example) and tilt them in a way such that different part of the beam arrives at the detector(a camera, for instance) at different time. Which means you convert time delay into space(position on the camera), and it only takes one pulse to get an autocorrelation trace.