I looked up your itinerary on the Disney Magic. I see that the Panama Canal cruise stops in Aruba. The itinerary says you will be in Aruba from 7:30 am-5:30 pm. As you have pretty much the whole day - if you get off the ship by 9 am and get back onboard by 4 pm - you will have 7 hours to explore Aruba.
The cruise terminal is downtown where the shopping is: Renaissance Mall, Renaissance Marketplace, Royal Plaza Mall, Main St, etc. If you into Casino's, there are 2 downtown - Seaport & Crystal Casino's.
I don't know of a Botanical Garden in Aruba. Maybe you are thinking of the Butterfly Farm.
http://www.aruba.com/whattodo/butterflyfarm.phpa
If you don't want to take tour from the cruise ship and want to shop, go to the beach and maybe go to the Butterfly farm, this is what I would do:
A short walk from the cruise terminal is the bus station. Take the #10 bus (says Marriott on bus) to the high rise section. Aruba buses are clean and safe. Roundtrip fare is $2.30 US per person. If you want to go to the Butterfly Farm ask the bus driver to let you off there. It is located across from the Divi Phoenix. From there take the bus up to Moomba's (less than 5 mins from the farm). It is a bar & restaurant between the Holiday Inn and Marriott Surf Club. There you can rent beach chairs.
http://moombabeach.com/component/ . There are also watersports vendors if you are so inclinded. After sunning and swimming, take the bus back downtown where you can shop before getting back on the ship.
If you want to see the island, I would take 1/2 day tour to give yourselves time for shopping downtown.
Whatever you decide to do, make sure you have plenty of sunblock and a small soft sided cooler for snacks and beverages.