Dont get stressed over its short wake up time, figure out how many narcotics it will take to fill its torpor from as close to 0 as possible, its about 1 stack for every 4000 torpor points. Place this in the inventory and allow your dimetridon to get as close to waking up as possible and then feed him all the narcotics at once. It will take just over 10 minutes for a stack of narcotics to take affect. This will give you time to look away and do other things.
Keep in mind, lower torpor (lower level dimetridons) may have less than 4000 torpor, in which case they will wake up sooner because they cant use a full stack of narcotics. Higher level dimetridons have closer to 8000 torpor, in which case you can feed them 2 stacks and they will take over 20 minutes to consume the narcotics.