Balloons drive me mad but I totally understand the wonder children have in toting them around.
Here is a quick and recycled idea that they might also find wonder in.
Take five newspaper pages, magazine or scrap paper will also work; just be sure the paper is not too thick or it will rip.
Lay the pages atop of each other. Fan fold all the pages end to end. Tie a cotton string around the middle and release the fan so it opens to a full circle. Gently pull each layer out so it puffs outwards, do this to each layer until you have created a pompom.
Tie the string to the wrist of child.
Add flowers or leaves for an extra whimsical feeling.