Ugh. Maybe save the arguments about exact wording and obvious implicit restrictions for its own thread? If memory serves, ascetic style is not allowed in PFS, and the creators have stated the rules are not intended to be interpreted in as literal a manner as those of us who spend our free time discussing them are apt to do.
OP: Ascetic style probably does help you, just ask your dm if it will work for him/her. In my experience, they will probably shrug and say 'whatever'. If you want to use two styles though, you will have to take additional feats to make that work.
Catfolk aren't allowed in PFS barring a single solitary boon, so gauging all discussion based on PFS is rather pointless in this instance. The discussion regarding how exactly claw blades, claw attacks, and various feats interact is entirely on point for this thread and critical to the completion of the OP's build. Hence, we absolutely should discuss it.
As to the actual problem the OP is trying to solve: I'm interested to see how this works out. I had worked on similar for a home game, trying to make use of the claw attack rule bits for catfolk monks, but ultimately discarded it all seeing I was jumping through multiple hoops to bring my claw attacks up to par with unarmed strike damage, which was decidedly worse than just two handing a temple sword or sansetsukon.
It appears you've hit on the Scaled Fist archetype, so that's a step in the right direction. I'll recommend grabbing Steadfast Personality to patch your Will save as best you can, and further suggest grabbing Vision Mastery for see invis or darkvision around level 5. See invis is a pain in the rear to get access to if you can't just cast it (personal range, so no potions, level 2 spell, so expensive for wands), and darkvision is just gravy once you can activate Vision Mastery more than once.
*switches to lurker mode to observe results of another's claw build*