Leeanne,
you seem to have two types of rockets combined in this activity outline.
The paper rocket (https://www.sfi.ie/site-files/primary-science/media/pdfs/col/dpsm_paper_rocket.pdf) uses a straw to blow a paper rocket, but is fiddly to make for very young children. I’m not sure where you would attach a balloon to it.
It has a nose cone (by folding the top of the paper over) and fins.
A balloon rocket (as described in rocket launch from this module’s resources) is an inflated balloon on a string. If you don’t use the string, then it is the same as letting an inflated balloon free. This is how we introduce it in our workshops at BCO.
I’ve not tried to add a nose cone or fins to this type of rocket, since, as the balloon deflates, they would not be fixed securely.