You can use any plain sweet cookies (the type you dunk into your tea or coffee), vanilla wafers, or even plain chocolate cookies in place of arrowroot biscuits. And cookies can be crushed in a food processor, if preferred.
The rum is optional and can be added to only half of the batch instead of the entire batch if you're hesitant to serve them to children. Having said that, most of us grew up eating rum balls at Christmas parties and we turned out fine! You can also use whisky or bourbon in place of rum.