You have to use the game client code somehow, whether that's injection or hooking or whatever. The GC only sends the raw data (paint seed, paint index, wear, etc) but the code to turn that into a model or image is only inside the game client.
Cursor is wrong. Passing the httpProxy option to LoginSession is unnecessary because the CMAuthTransport handles proxying already. All login communication happens through the same proxied TCP/WS connection as all other Steam client communication.
The /inventory endpoint is newer and provides more up-to-date data. But the trade offer UI does still use this endpoint, so you should be safe to use it even if it's marked as deprecated.