I be taken an satchel bag to walk around disney park and since up only me and my mum going disneyland Paris on 13th-17th October 2014 will have take my satchel bag on all the rides(even the roller coster and go fast)
I always take a small handbag that goes across my body and keep it on whilst on the rides ( normally under my coat ).
Faster rides I take it off and put it on the floor , out my leg through the strap and keep hold of the strap .
It always stays put on the fast rides like space mountain and rock and roll coaster .
I have a small PE-type drawstring bag that I wear over my shoulders. When we go on rides, it is either on my knee or between my feet. I have even been known to sit on it or put it behind my back. It has always been very safe.