I have done the T7<->Hyatt walk multiple times the past month, and with the Sheraton ~5 min past the Hyatt, it's very doable (esp. if you feel like stretching your legs before or after a flight).

I am not familiar with any underpass to be wary of - there are stoplights w/marked crosswalks at all key points (going to/from T1 to the garage, T1 to the main N/S sidewalk, and then crossing Sepulveda.