Can you bring toys to Celebration Key? What about strollers?

My family, including our 4 year old, will be cruising in May and stopping in Celebration Key. Can you bring sand toys for kids or pool floats?

It seems like none of this is allowed onboard the ship but I can't seem to find info about taking these kinds of things to this port?

Additionally, anyone have experience with a stroller at CK or other Caribbean ports? We have a Baby Jogger City Mini GT2 I was thinking of bringing because our 4yo loves strolling over walking, whereas my husband and I would rather walk 2 miles than pay for a taxi.