As such for transmission of genital wart skin to skin contact is necessary for transmission . It is hard to give exact answers about HPV, becuase as a virus, it can effect different people differently.
But as such theoretically there is small chance of contracting the virus to other part of body from skin to skin contact is there.
As such you should avoid touching your child without washing your hands .
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As per this website
HPV is Quite contagious, these viruses enter the body through small cuts or abrasions in the skin and can be transferred from one body part to another - say, from hands to feet or face - or from person to person. It is possible to become infected by wart viruses from damp towels touched by an infected person or to pick up the foot HPV virus from the floors of changing rooms or showers