To answer the original question...yes...you can wear fanny packs on the attractions. Just remember...they can NOT impede the restraints in any way so make they are small.
I have a small bagalini bag. Can be worn around waist,or used as a bag off shoulders. no problem on rides. Just make the bag as small as you can. I was even able to go thru the security lines that read " entrance with no bags" I just opened it up and they waved me on, much faster. Rode Harry Potter no problem. I love this bag but of coarse it's for gals.Cargo pants might be a good option too.
My wife has used a fanny pack for years to carry all of our "stuff"; tickets, money, room keys, small camera, etc. and she has never been denied access to the rides.