A few notes. First, a shuriken is a thrown weapon (sometimes called missile weapons), not a melee weapon.
Secondly, I have two runs on record where I used only only tier 1 gear, with additional stipulations. The first was a warden run where I finished with strength 6, having used no strength potions and equipped two cursed might rings, on in the caves and one in the halls. For that run, I ended with +10 armor to avoid encumbrance, but both my +3 gloves and my +5 bow were too heavy, though I used then anyways.
The second run was a completely potionless/scrolless rogue run. I ended with the same gear I started with, and didn’t end up with any additional rings or artifacts either because I couldn’t confirm any were uncursed. Now, I have done potionless/scrolless with three classes total, but in the other cases I either had a lucky armor drop (leather +3 for Warden), or I found a great shield (for mage; I couldn’t attack with it, but melee combat wasn’t a good idea anyways so that wasn’t really an issue), so that rogue run was the only one of those that was all T1.
I feel the obvious strategy is to try and find a ring of elements and get it pretty high leveled.