Hayate is i10/i12/i14 (High/Mid/Low)
His jab is -1 on neutral hit and -2 on block, and his 2P low is +0 on neutral hit. In CQC, his bigger threats in this match up are his 6P and 8P+KP/2P+KP. 6P is his only i12 frame mid, however, but 8P+K is his special step that gets around linearity and can punish it with the mid punch follow up for a stun (mindful Hayate players will use this step correctly though). So Ayane's neutral K plays a factor in this match up for two reasons; it stops his 8P+K step and counter hits his 6P, essentially killing two birds with one stone.
Once you make Hayate realize you have that option select in neutral CQC, the Hayate player may resort to jabs (and strings), 1P (hi crush), 1K (hi crush), or more 2P usage to shake things up. If this is to happen, take this as an opportunity to see where Hayate's next retaliation is going to be, and how often it'll be.
1P is +16 on counter hit, but -7 on neutral hit. If it hits on neutral, you have lots of retaliation at your disposal, 66KK4 becomes a thing after that -7 on free cancel. But 1P has follow ups, 1PP (low P/mid P) and 1PK (low P/low K).
1K is a single mid kick strike that has crouching properties, so Hayate is going underneath highs, so it is a hi crush. +3 on neutral hit, so do not strike retaliate after that hit confirm. +23 on counter hit and threshold.
Hayate's strings are just decent on block for delay and free cancel. IMO his best two are PP6[P] and PP2KP. PP6[P] is a guard break and leaves him at +3, he also has PPP[P] and has the same guard break for the +3 so be mindful for full string into guard break. Once you're used to seeing that guard break animation often, you can strike retaliate on reaction, however.
PP2KP has a solid delay after the PP2K, it's pretty hard to tell if Hayate is going to do the mid punch or a throw, the low sweep is not that difficult to see though (although you're probably going to get hit with it online anyway). He can cancel into the wind dash as well by doing PP2K6P+K, but once you're used to seeing it, you can 4P him on reaction.
Here's Hayate's P and PP strings so no one's in the dark about them.
On block;
PPPP is -11 (HHMM)
PPP[P] is +3 (HHMM)
PP6PP is -11 (HHMM)
PP6PK is -7(HHMM)
PP6[P] is +3(HHM)
PP6[P]66 is -42 (HH) in neutral, not good on block at all. Only during okizeme and threshold mix up. You can BT6P him if he does it on block.
PPP[P]66 is the same deal as PP6[P]66. (HHM)
PP2K2K is -15 (HHLL)
PP2KP is -11 (HHLM)
PKK is -13 (HHH) and you can strike retaliate with a low inbetween it.
PPKK is -4 (HHHM) but has does not jail at all, so you can hold the high kick or mid kick ender.
Hayate at range is the where the fight actually is, if I'm to be honest. Ayane can fight Hayate at range very well, and so can he. But Ayane has a little more than he does for range. The wide array of Integrated Movement and other certain tools make things difficult for him to approach. Smart use of Haijin Dash/fients and spins will always make it difficult for anyone to get in. But for Hayate, he is looking for a reason to utilize the following;
66P, 3H+K, 214P, 236P, 236K, and 3K.
66P is very self-explanatory, it's what he has to go in with head on and the damage on it is solid (25). 66P has follow ups as well, 66PP can be done or it can be charged for +3 on block (something I was caught off guard by against Shade Swifteye at SCR earlier this year). 66P2K goes into a low sweep. 66PK goes into a mid kick, unsafe it blocked.
3H+K is always another Bread n' Butter ranged get in tool for Hayate since it's so easy to put on the screen. Has a low sweep follow up, but the mid punch shoulder cannot be held if the low sweep is hit confirmed, so it is a natural combo. 3H+K has no delayable frames into the low sweep, however, so if Hayate free cancels, you can low throw him on reaction.
3K is i14 frames and does 25 damage, it's also +1 on neutral hit but -3 on block, ideal at close-mid range.
236K is a high kick that's solid for whiff punishment and a get in tool at the amount of distance. +1 on block as well
236P is his best whiff punishment, 40 damage and knock down.
214P is there to catch your sloppy footwork.
My personal favorites for Hayate at range however, are his PP6[P] and 9P[P]. Both are solid at their respect ranges for knockdown or +3 guard break. So if Hayate is jabbing or doing 9P at ranges, beware of the strike range. Not a lot of Hayate players use these two this way though.
Hayate can feint with his wind dash as well but he really has to range that out correctly, otherwise he can get slapped for it.
The fight at range is basically going to be a question of how well you can keep Hayate out, and how well you can maintain the neutral game at range. Ayane's K can stuff a lot of his high and mid strike approaches, due to i12 frame speed and that 27 neutral damage (something I didn't utilize very well at SCR vs Shade but I've reviewed those sets and am completely aware of how solid it is in this match up). But in order to do that, you have to be pretty masterful with neutral K at range because it does leave your back exposed. Awful whiffing gets you whiff punished, 3H+K can do the same thing.
K, K(delay)K, 3K, 3K(delay)K, 3P, BTPP, BTPK, BT2P, BT2K, BT6K, BT3K/BT3KK, BT4H+K, PPK, PPK(delay)K, PP6P, 6PK, 2P and occasional (but well ranged) 66KK4 are all the tools you'll be utilizing at range in this match up. But you have to pick and choose which is best against said player and the situation.
Your whiff punishment never changes, it's going to be the usual 4K, 236K, BT6P, 3H+K, 1P+K K, 1P+K P, etc. Whenever Hayate makes a bad whiff, punish it, you want to do your best not to let bad whiffs slip by because you want every opportunity to do damage.
Summary; P > BT8P is always your best friend in any match up. Do not let Hayate control the CQC with his 6P, if he jab retaliates a lot, make good use of your hi crushes. Be careful at range, Ayane may have a little more than Hayate but that does not imply you can be reckless or get sloppy. Stay patient, punish his mistakes while ensuring you keep your own to a minimum. Do not let him utilize his throws a lot, or you'll lose.
All in all, it is a pretty fair match up.