Yeah subbing sounds like your best bet. I've never had to use the handwarmers to keep the bottle at temp. Just got it to about 99 degrees in the microwave and then just stored it in my crotch. I've got one of the mouth thermometers just to double check the temp strips on the bottle and they work good. I would keep mine in my sock for the drug test. Have never seen the little stick on thermometers available.
If when you take the test your temp is too high when you pour it into the collection cup, blow on the urine to get the temp down. If its too low rub your thumb against your clothes for a couple seconds and then place your thumb against the temp strip on the collection cup. When it reads 98 degrees step out of the room.