I think this is generally a bad card when things like Machete exist, especially as Machete only takes up one hand slot. You can assemble things like Steady-Handed or Knight of Swords on specific investigators to help you succeed by the right amount for its test, but even then Katana exhausts when using its +2 damage option, so what's the point in building an engine around it when you're going to get less damage than 3 actions on a Machete? The +2 if you're not bothered about the extra damage is okay, but if you're not bothered about the extra damage then the humble Knife becomes a cheaper and less resource intensive option.
The interesting bit therefore is the fight test. While people like "Skids" O'Toole can use this, there's better things which can go in his hands (e.g. if you want to do fighting, the new British Bull Dog is nice albeit ammo intensive). For this reason I'd recommend:
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Lily Chen. Lily has usable especially with the relevant Discipline, she can use Enchant Weapon on Katana to do 2 damage as fast (though note that does not add to the test here, you just get the damage) and she can take additional non-niche weapons with Occult Reliquary (e.g. Blessed Blade ••••) and/or Bandolier, or just use Brand of Cthugha. The new Wolf Mask can give means to boost further, as can Combat Training. Overall this is a fairly good option, but it's also painfully clear that the experience costs getting this all to work really mount up, so you've got to care a lot about that 2 damage (as there's easier options for that as well, for example Blessed Blade ••••, Ancestral Token and Nephthys, or even just a couple of Beat Cop ••).
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"Ashcan" Pete. Pete has usable , which is easy to boost with cards like Peter Sylvestre, Track Shoes, Moonstone and Sparrow Mask and can un-exhaust the Katana with his ability. While this is good, especially as the means you can evade when needed to, it naturally stops your hands from other useful assets (Thieves' Kit, British Bull Dog, Hyperphysical Shotcaster). You could rely on spells to flex, such as Clairvoyance and Sixth Sense, but then that's a lot to juggle and Pete doesn't have ways of guaranteeing these come into play (e.g. there's things like Arcane Initiate, but with 2 Katana, 2 Clairvoyance and 1 Sixth Sense there's no room). Still I think this is the most interesting use for Katana, and Duke allows you to further take chunks out of enemies. It just again feels a bit gimmicky rather than a naturally strong combo.
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Charlie Kane. Charlie can also unexhaust assets with Bonnie Walsh, and can access Beat Cop •• for more fast damage. Even so he's more awkward than either of the other two in getting this working.See comment below.
The last thing I'll say about this card is its resource cost stinks. 4 resources for two kinds of actions which are hard to get working properly? No thanks! Overall I'd say it has niche uses on some investigators around its action, but is otherwise outshone by easier to use fight assets which are cheaper and take up only one hand (e.g. Machete).