Talking to BiL, a retired dog handler from Avon and Somerset, one problem was carrying a strange dog. All DH had to repeat the test at the annual refresher. They carried their own dog but new recruits had to carry what was available. The dogs were not always happy.
The technique was to hold the legs tight and pull the dog tight into the back of the neck.
Not all men pass the tests either. He said they had one card though against people crying off. They had an Army female PTI and if she could do it . . . Apparently all the instructors took part in the tests too. The biggest problem was some recruits were not as fit as they thought they were.
He was ex-RN FAA Field Gun team too - all tea and sympathy like.