What did he sleep in before? We put our children into normal size single beds around the age of two. Never fell out. Would often get out though!
We had a bed cot, but never used it as a bed, because there was always the next baby coming out of the Moses basket. My last one went straight to a bed, as she had seen her siblings do.
If your grandson had a cot at yours, can you just take the sides off? The danger isn’t falling out...it’s what else is in the room, open doorways etc. At nearly three, he should be fine in any bed I would think.