Just a idea
If as you said that the main cold sweats during the night have stopped, but he can still get them before waking..
This could show that in he could be getting a low but futher into his sleep pattern, it might be a idea to take a BG before he retires to bed, then if his cold sweats are prettying well about the same time lets say around the 7am ish, for agrument sack, then take a BG at 6am and then one when he would wakes... And slowly over several nights take one about a hour before the last night, this should give some indication to way his BG might be raising and falling and raising again..
Given a bit more info, to decide what his best action to over come this might be!