And it's not hard for Hawking's hired aides and nurses (who of course existed) to do so, either. As an able-bodied person whose cat very much does not want to go into the cat carrier, it's not that hard, if you use your brains. You feed them a little gabapentin, whose existence they cannot even comprehend (and you know they don't know because you have used your mind to model the cat's behavior like 'do cats understand drugs' or 'do cats like eating treats'), and when they are drugged, you put them in the cat carrier. Done.

Turns out, 'brains' are useful for things like 'inventing and manufacturing drugs'.