I lost a fair amount of weight before doing my one and only RunDisney 5k. I was over 300 at one point. (I've done longer non-Disney races, but any more races will likely have to be done in a wheelchair).
Since I didn't want to destroy my knees with my excess weight, I focused on getting all my muscles strong and balanced by hitting the weight room. I felt out of place, especially when many were lifting heavy and quick and I was going slow to focus on brain-muscle communication...but I persevered and saw great improvement.
I also did hill training to get my heart rate up really high without a lot of pressure on my joints.
Lots and lots of balance training. Simple, boring, but very important.
For weight loss I did swimming and a low carb diet (really helped with food cravings). I got a coach and improved my stroke technique since I wasn't a strong swimmer.
I've also never been a runner due to physical limitations. I walk quickly and with proper technique, and have in the past out-walked numerous slower runners...especially those who started quick and then tired part way into the race and their pace slow down. The pace required for a RunDisney race is very doable if one has trained to do it walking.
Basically I did everything but run to train for a running race. I've also never been injured or had a setback due to improper training.
I'd recommend getting properly fitted for running shoes by a boutique running shoe store with a wide selection. You can always buy the same kind of shoe later for cheaper online, but getting a proper fit is so important and paying full cost for a shoe the first time is worth the expert fitting that comes with the purchase.
Proper clothing is a must too if you have excess skin from weight loss. Something similar to compression tights really helps keep the jiggle down, to put it bluntly.
I hope you are able to find a path that works for you to get fit enough to do a RunDisney race! It truly is an amazing and fun experience...not just the event itself, but meeting all the other runners.