I would highly advise against it. While its not very likely someone will be targeting systems running the game through Proton, its also not out of the question and malicious code can do serious home even through Wine/Proton.

Most vulnerable COD games have community patches and servers to avoid this. Theres Plutonium for WaW, BO1/2 and MW3, a community patch for BO3, and AlterWare for MW2/3, Ghosts, and Advanced Warfare. I've used Plutonium before with Proton and it worked great, and AlterWare has instructions for running it with Proton.

Besides the security these community launchers/patches have quality of life and performance improvements, they're definitely worth using.

Wine/Proton isn't designed to be a sandbox. A motivated enough attacker could make an exploit that checks if it's running in wine and do some wine specific stuff.

Even if you do manage to sandbox it from your root filesystem, it still needs access to your Steam account, which an attacker could compromise.

Maybe check out emulators if you’re okay with controllers? I just downloaded CoD MW2 for Xbox 360 on my Steam Deck because I can’t play with a keyboard and mouse and the controller scheme just works as it should.

I use Xenia Canary and there is a netplay version too.

Plutonium works fine on linux and is the go to if you want to play old CoD games.

Sign up for Plutonium and add it to Steam, worked like a dream on Linux