I´d agree with the other posters (especially the part about not mentioning about it for a while, now that the subject has been brought up.)
One suggestion I have made that many people have said worked well for convincing is to pick out a place about 2 miles from his house that he is familiar with. Ask if he could walk there. He will most likely look at you like you have grown 2 heads. If he doesn´t and says he could walk there easily; ask about walking back and then doing that every day while you are there.
Estimates range from people walking between 3 and 9 miles per day at WDW Some have actually used a pedometer to measure and most people go way more than 3 miles, especially when you consider that it´s more than a mile just to walk around World Showcase (along the water, not to go inside all the countries). And it´s a similar distance to get from the park entrance to the point of entering WS. If he doesn´t believe you, you go on google maps and actually find distances.
Another thing to think about is whether he would be able to operate an
ECV in the parks. It may take a lot of effort for him to be watching for pedestrians and be steady enough to drive. In that case, a wheelchair will be better for him.
As time goes on, it may be helpful to find out why he doesn´t want to use one. If he is stubborn and prideful, different methods of convincing will work than if he is afraid he can´t drive it. He may be afraid he will hold you back or he will be the only person in one, so everyone will look at him. He may be concerned about the cost. Any of those things can look like just being stubborn.
My FIL had very bad hips and knees, but would not rent an ECV for many years. Looking back, I know one of the things he was most concerned about was whether or not he would be comfortable driving one. The last few years, he did rent one, but never did feel comfortable driving one in MK because it is much more congested and there are more children.
After the first year of renting an ECV in Epcot, he said he wished he had done it years ago. It was the first time in years that he had actually enjoyed a day in the parks and ended the day without pain.
Another thing that sometimes works is thinking about energy like a checking account. Each morning, you have a certain amount in the account. Everything you do has an "energy cost" attached to it. There are things, like climbing in and out of rides, where you can´t do anything to decrease the cost (other than not riding). There are other things, like getting from place to place and waiting in line, where you can decrease the cost a LOT by using a wheelchair or ECV. Some things, like eating and sitting down to rest, puts more energy into the account. But, if too much is spent on doing things like just getting around, you end up needing too much time resting to get enough energy to finish the day or there will be no energy to have fun with. Too much energy used begins to use energy from the next day´s account, so the next day is begun with a deficit. Since most people can imagine what happens if a checking account is overdrawn, they can imagine what happens when too much energy is used.