Collaboration
I'd be happy to work with you. Let's talk about the basic premise. You have some choices:
Do you want to have a character that we already know go through the experience of losing mobility and then regaining it, but with a greater sense of appreciation for how different the world can seem from that vantage point? That's a common experience for people who lose mobility temporarily, and you could use any one of the muppets that you wished for this story.
If you'd rather, you could create a totally new character who would mesh up with whichever mup-universe you chose to use (TMS, SS, FR). That gives free rein on creating a non-tab* character who could be ideally suited to the story you want to tell. This is also harder, since you'd be starting from scratch.
You could also decide to veer off from canon (established muppet fact) and/or fannon (sortof, kindof, semi-established muppet pseudo-fact that comes from the assorted fan writers here at MC) and pick an established character--like Kermit or Fozzie--and make the change permanent. So, for the purposes of this story (or universe) if you like, the character you chose would remain in a state of limited mobility permanently. This can also be a starting point for a dynamic story.
Does that help you clarify the story you want to tell? Also, you probably have some idea of how you want this to progress. Will mobility be lost as a result of an accident, or illness? Will the character have some time to prepare for this loss, or will they learn to cope with it after the fact? Do you want to portray them as always chipper and satisfied, or more realistically, in order to show the steps that most people go through as they adapt to a permanent life change?
Hope I haven't flooded you with information, dear. Let me know what it is you'd like to do with your story and we can move forward as schedules allow.
*temporarily able-bodied