The flowing lava area in the park changes from day to day and the park rangers have up to date information. Ask them before starting out on any trail. Sometimes you can view it with just a short hike, sometimes it is a long hike, sometimes you can't get there by foot at all. Sometimes the lava gets out of the park, but it's mostly been in the park lately.
Personally, I don't think it would be a wise idea to have anyone who isn't agile and sturdy walking across the lava. Because the lava viewing area changes from day to day (sometimes from hour to hour) there isn't an improved trail to go look at it so it is really rough in areas. And the a'a lava is very sharp. They usually try to have the trail across the pahoehoe lava but that isn't always possible. A'a is the rough spiky lava that cooled while being tossed in the air it is really sharp and loose on the ground. Pahoehoe is the smooth lava that cooled while puddling on the ground, it is much nicer to walk on although sometimes you can break through the crust. Cows and bulldozers have been known to break through and fall into underlava holes although that wasn't in the park area. The park rangers are pretty good about marking a safe trail.
The Thurston Lava tube would be a nice hike for a youngster, although it is more of a walk along a nice trail winding through the fern forest and through an underground lava tunnel than what you are probably thinking of when you think of "volcano".
Lava rock cuts are treated like any other trauma of that type. Check the standard emergency procedures for jagged cuts. Let it bleed enough to clean it out or irrigate it to clean it out. Pressure on it to stop the bloodflow. An antibiotic ointment and a bandage to keep it clean and have a qualified medical person check it out when you get off the lava. If it is a deep cut (and you can get that from just falling on the lava) then you may need stitches. Basic emergency medical advice that I've heard is "start the breathing, stop the bleeding and make them lay down". But, I'm not a medical person, so my advice is merely uneducated advice and what I consider common sense it may not be what you need at the time.
The Hilo Zoo (The Panewa Rainforest Zoo) would be a nice picnic spot for a youngster, while you are in the Hilo area. It is a small zoo and appreciates donatations at the door but is free and a great place to take a picnic lunch. There is a white tiger and lots of peacocks wandering around. There are a lot of botanical specimens as well as the animals. They just added a frog display that a five year old might like if they are interested in critters like that.
Have fun and be safe,
A hui hou,