Hi Chuds and welcome to the Dis,
Getting around without a car in Orlando is not the easiest of tasks but really depends on where you are staying. Onsite at Disney or off? If you are on I-Drive then the I-Ride trolley is great for getting to Seaworld, Universal etc. but your wife may have problems getting on and off if she has mobility problems. Many of the I-Drive hotels have free shuttle buses going to Disney and the other parks but you would need to check on this before you go.
If you are staying onsite the Disney transportation system is very well organised for the Disney parks but you may have to resort to getting taxis etc. to the other parks. I am sure there is a company that does excursion trips out to Kennedy space centre but for the moment their name escapes me...
If you are staying in a villa, forget it - you need a car.
We have taken my mother, who is partially disabled, with us for the last two years - she uses and electric disability
scooter in the UK and the airline flew it over to the US free of charge. These scooters can also be hired in all the main theme parks.
I do honestly think that we would have struggled without the car though, and would urge you to consider hiring one if it is at all an option.
If you let us know exactly where you are staying I am sure someone will be able to give more specific help and advice.