a hat on a string is hardly a strangulation hazard everyone does that
I for one always refused to use those strings for anything and just jammed the hats onto my head. Then again I was paranoid enough as a child that before I could talk, when my Mom tried to feed me a banana, I kept rejecting it until I watched her eat one. Then I accepted eating bananas as "not dangerous".
The school hats for kindergarteners and the youngest of elementary students all have the string on them (You know, those round yellow ones). They upgrade to regular ball caps later, though.
Go to that store over there first,then after that...