Bike helmets here recently are no longer approved for any kind of ice skating. Bike helmets do not have protection as much at the back of the head. A typical fall in skating is when you get scooby doo legs and feet fall from under you and then boom your laying on your back and the back of your head potentially smashing the ice as well.
In saying that, in your situation, I would for sure wear the bike helmet as it is better than nothing. Plus I am sure you will be holding him? Skating is part of our gym curriculum so they skate every Friday all winter as an arena is near us walking distance. Skating is a big part of Canadian culture as you probably gathered from the recent Winter Olympics.
It is also highly recommended for children to wear face guards such as a cage style. I feel ds is a confident skater now at this age as he has been skating for 5 years but I still insist on his skating helmet as I do with scootering and rollerblading and biking.
My main worry for ice skating at this age is typically if he falls, it is face forward doggy style with the face potentially hitting ice, I fear a broken nose and of course smashed permanent teeth!
This is what is required here at public arenas, with or with out the cage. We still have him wear it on frozen ponds and outdoor ice rinks: