I think you should totally take this up as a challenge to build yourself! Wood is a great material to work with to get started because you can cut and shape it with some affordable and fairly safe power tools. I think you could build this project with just a power drill and a jigsaw. If you’re interested in 3D modeling at all, you could even try downloading Google Sketchup, it’s a relatively easy to use 3D modeling software and you can get up to speed pretty quickly by checking out of youtube tutorials. This is another way to prototype your idea before you start building.
What I like to do is to go shopping for material ideas and things like the handles and hardware at home improvement or hardware stores. You could also stop at a sporting goods store to look at rubber materials like you were thinking. You’ll get a ton of ideas just spending some time walking around and seeing what’s available. Instead of buying materials right away, take a picture of them in the store and later you can look at all your options.
Good luck, have fun, and don’t worry about getting it right the first time. Go into it knowing you’ll make it two or more times until you’re happy with the final result. It can be frustrating but it’s not a waste because you’re learning essential skills for the next build you do!