As Walter has said, Wreck diving with Penetration or Cave Diving (I know you did not ask but they are similar and might as well cover both) is a specialty course you should not be taking until you are very comfortable with your skills and have logged a number of dives in a variety of conditions. Most wrecks will be at deep depths, many beyond the normal limits of recreational diving. IMHO 100-200 or more dives would be highly recommended before going to Wreck or Cave Diving. Wreck Diving, or Cave Diving both require spot on buoyancy skills, and a total mastery of basic and advance SCUBA skills along with special training and equipment.
As Walter has also stated the answer depends on your abilities. Wreck and Cave Diving are both very advance types of diving presenting their own special challenges and requiring special techniques and equipment. Silting out of the wreck or caves is a hazard that all Wreck or Cave divers face. If the silt on the wreck interior gets disturbed visibility often goes to zero (from what I read) which could make finding your way out challenging. To avoid this Wreck and Cave divers learn special finning techniques to avoid even the thrust off their fin tips from disturbing the silt. If mobility of the lower limbs is an issue then this will present a challenge. Both environments are also noted for limited maneuver space which would present a challenge if the diver depends on their arms to swim.
Is it possible for you to get a Wreck Certification? That depends on the individual diver and their abilities and skills.
