The only thing you might need is lemon oil. Tung oil is used for naked wood, of which your guitar has none, except the fretboard, which is rosewood.
Lemon oil is used for rosewood to keep it moisturised to prevent it from swelling, shrinking and cracking.You don't need to use it often; I use it every time I restring my guitar but you can do it every couple of restrings if you prefern.
Most lemon oil (like Dunlop 65: Dunlop - ULTIMATE LEMON OIL
) comes with a felt applicator. Basically, you rub it on the fretboard between each fret, leave it for ten minutes, then remove it with a dry rag or cloth, then put strings on as normal.
I have an old
picstory over on ss.org you can view here, which sort of outlines the process:
Restring/Fret Polish without steel wool - Sevenstring.org
Ignore the stuff about fret cleaning unless you fancy having a go at that too!