This seems quite doable, but keep in mind that it depends on how you want to use the player.
For example, if you want it to keep playing while changing pages, it would only work if your Shopify theme supports AJAX navigation.
Besides that, the implementation is simple: I would add the player and its dependencies as JS scripts. And add further scripts and CSS to customize the looks and the way it interacts with the rest of the site. (For example, you may want several instances of the player at the same time)
About me, I've made several personal projects with React. In fact, I've made some contributions to the core repository on Github. I favor solutions like Redux and preact.
For what it's worth, I'm familiar with Node.js, and its build tools like Grunt and Gulp. I'm a big fan of LESS/SASS for front-end, and an advocate of responsive design and flexbox.
Let me know if I can be of help on your project.