Many families don't want to be bothered with that step. I say good on you and tell them you will only employ someone who is willing to work and do it the legal way. Otherwise, its a no-go!
Easy games and books.
Meet outside the home first. Somewhere public such as a coffee shop where there are lots of people around before you even consider inviting them to your home. Install "Nanny cams" that you can view remotely once a caregiver has been hired.
Hands on would mean assisting the client physically as needed. Companion care means providing companionship and assisting with needs but not necessarily any thing physical.
The Care.com Community is an advice-sharing network for parents and caregivers.