It kind of depends on exactly what the restriction is you're giving yourself. Questions that come to my mind are
1. Is "unarmed melee" a game mechanical category you have in mind, or just vibes? Some combination?
2. If the former, what does that mean more specifically? Are you allowed to use anything that has the melee tag and not the weapon tag? Are spells allowed? Are charms? Do you want just the rusty knife in your main hand, or is a stat stick of some kind okay? What about your off hand? etc
3. If it's vibes, how specific are we trying to be? You mentioned Lightning Fist. Are we only using moves that specifically refer to punches/strikes with limbs? Are we allowed charges, tackles? Can we use things that aren't physical strikes but are still sufficiently martial arts flavored (Kiaijutsu, for example)?
4. How much are you willing to bend your rules for the sake of convenience? I'm particularly thinking you'll have an easier time if you allow yourself Mirror Stance than if you don't, for instance
5. Is the scope of your restriction just the combat relevant stuff like powers and equipment, or something broader? If your monk is obligated for rp reasons not to play nice with certain NPCs that could help you, not use some consumable items or drinks and so on that would probably impact how you want to build.
In any case I think the obvious starting point for you at least early game is probably setting up camp at Zo's until you have the Silver Mask and a flexible suite of at-wills at least.