I don't have any suggestions for sheeting, and you are correct plywood would warp soon after laying in the rain, and would also rot.

Something that you might consider is making a more permanent pathway with something like pavestones. This might cost more initially, but you would have a semi permanent solution that could also make that area of your yard more accessible for other activities in the future. Handling the pavers and leveling the ground is labor intensive, but it could be worth it, to be done after the initial install. Just a suggestion.

Thank you for your feedback. I do like the paver idea, the main thing is getting a reliable person to do it. Maybe there's a site that I can find local professionals. Not sure I will go that route but I will think about it, thank you!

A poured gravel (21A) that is compacted with a plate compactor would be just fine for a wheel chair. Much like a concrete sidewalk, the compaction would make it a hard enough surface for you to travel over without the concern of getting stuck or needing to do extra work with your arms. You could border this with landscape timbers.

Check this, site gives shipping discount for email sign up. I saw the wooden one at Tuesday Morning store but was OOS when I went back.

http://www.improvementscatalog.com/wooden-walkways/363468

http://www.improvementscatalog.com/wood-look-rubber-outdoor-pathways/garden-decor/walkways-garden-bridges/329966