Like what the rest have mentioned, HFMD is highly contagious and could spread through contacting the body fluid of the affected person. I can understand how you would like to take your child out for some fresh air especially when he is probably very uncomfortable with this. However, you can probably opt for a short walk in the park instead and not having on the playground to minimize the risk of spreading to others. Hope your boy gets well soon! And take care of yourself as well because adults could also get infected.
I think whenever our child is sick, the best is to stay at home and rest until they fully recovered. Not only you can monitor him alone without external contact going on, but this could also minimise worsening the situation and the same time prevent the spread of the disease. HFMD spreads from person to person by direct contact with the nasal discharge, saliva, faeces or fluid from the rash of an infected person. Read on more here to know about HFMD: http://bit.ly/1rjTNB3
Even if he doesn't come in contact with other children, he can still touch surfaces that might have traces of the virus. Perhaps you can keep your child clear of places that could be hot beds for HFMD like playgrounds and parks. If it can't be avoided, just make sure your child doesn't rub his eyes or put anything in his mouth that he shouldn't. Sanitize his hands and get him to take a shower as soon as you get home.
Your child still will be in risk of contacting the hfmd if he touch the places where kids with hfmd touched before. Just to make sure your child don't put his hands into mouth or rub eyes or nose and sanitise your child's hands as frequent as possible in the park.
thanks