Blades is easily the best way to break the game. Add some Cyberware on top and you are a 100% crit, lifedraining samurai really. Cool is however NOT a support attri for Blades. Its support for the Monowire and takedowns, in other words, full stealth / Agent 47 style.
Support for Blades is found in Athletics so Body. I ran 18 reflex and 12 body which was great balance, it also opens up some health boosts in cyberware and since you lifedrain on counter and kill, a health pool is vital.
You mentioned ColdBlood but I dont recall seeing it work proper and its not really that OP I think because the perk investment is huge while weapon specific bonuses are generally not only higher per point, but also passive/permanent and not related to stacks. Im sure on higher diff Cold Blood could scale well in longer combat sequences.
Also: Try out Sandevistan to teplace your cyberdeck. You wont regret it. That, double jump and jump-dodge cyberwares and its a whole other game
What youve got in yiur head as katana playstyle... yes it works perfectly fine. You do miss out on the whole silly AI thing, heads just fly off if you even look at them funny...
Oh yeah and the melee weapon vendor in your own appartment tower has a level scaled legendary katana, should you need one. Mantis Blades however may have a different cool factor but do have higher base damage, level scale with you and a leap attack so def better than katana and even cheaper in the long run as you only need one up to level 50. Street Cred 50 gets you legendary versions.