You may have trouble getting something with a similar color. Can also try a plywood specialty shop if you have one nearby. RVs use luan plywood for it's lightness but is 1/8" thick like other "ordinary" plywoods.
Wall plywood in RVs is stapled which is kinda good because it makes it easy to pull off but you could use some PL400 adhesive and use a few dollops of it on studs. If you overdo it, you'll have a big job to get it off. PL400 will be available where you buy plywood (except at RV places).