The natural gas sweep, the longest part, during the shut down process is very important for getting all of the sulfur out of the catalyst beds. If you don't get the sulfur out of the unit well and don't change out the catalyst you can definitely have a thermal excursion (i.e. fire) inside your SRU potentially resulting in equipment damage and excessive SO2 emissions when you start up firing excess O2 on natural gas. Its generally not a good idea to shortcut the hot soak and sweep steps on a shut down as it will tend to cost you more in the long run. Brimstone, and probably others, have published some papers on this subject; try Googling them.
One effective method I have heard to shave some time off an SRU shutdown is to do an assisted cool down. Typically you spend quite some time just blowing air through the unit with the blower to cool it down. I've heard of at least one company, BJ Services, that can in some cases greatly accelerate the cool down process by fogging nitrogen and CO2 through the SRU.