Make sure his ears are clean, eyes free of discharges and feet free of mud-balls between the pads. Regular grooming and general handling will make your wire easy to cope with if he has to visit the vet for any reason. Perhaps it would be better to get another puppy from a specialist breeder if you want a companion for your pet. Generally, Wires are very healthy dogs and, given a good balanced diet, plenty of exercise and mental stimulation, should be no more prone to ill-health than any other dog. Simple precautions like not allowing them to climb stairs and supporting their backs when you pick them up really are important.
Some Wires can be prone to itchy skin or grass allergies.
Always seek the advice of your vet if you are worried. There are no particular inherited diseases that are currently causing concern in the Breed. Two dog puppies, growing up together, will almost certainly fight when they are older in order to decide who will be top dog. You may need to get one, or both, neutered to help avoid this. Generally, we don't recommend people should have two dog puppies.