The first thing that annoyed me was when it was on FD, and whenever I'd UpB to recover, he'd be somewhere in between the middle of the stage and the ledge where I'm recovering and using his needles(No jumping needles, just standing there and throwing them).
Yeah this doesn't work, the best advice I can give is to try to reverse upB, even if you use your regular upB and eat a needle to get close to the stage, do that and then DI in and do your best to sweetspot with a reverse upB, CF can go surprisingly far down and still grab the ledge, and needles won't hit you.
FD is a good stage vs Sheik, once you get better at the matchup you'll see that her without platforms is a blessing.
The second thing that got to me was I could literally never hit a knee on his Shiek.
Yeah Sheik is a pain in the ***, obvious knees will either be ftilted or shieldgrabbed as you pointed out.
What you need to do (and you're going to need to do this A LOT in Melee in general) is work on being smarter and finding openings. Sheiks that jump can get hit, Sheiks that don't jump (like this one) will not get hit by many of your aerials at all.
Find out what she does vs your running approaches. Some Sheiks will just ftilt at you no matter what you do, others will grab, and some tend to shield a lot. You can punish all of these things if they are predictable, that's the good news.
vs ftilt, you can run and shield out of your run, block the ftilt and then you have decisions to make from there. Generally she will just ftilt again, over and over. Learn to wavedash out of shield, close the gap, DI down (in shield) and mash A, you'll get the shieldgrab. If they do tricky **** like jabs and dsmash you can either roll away or even dair/knee the dsmash with the right spacing/timing.
Nair out of shield is a good idea if you know another ftilt isn't coming, but even then sometimes it will hit her. You need to be REALLY fast though, i.e. know the shieldstun ftilt gives you, jump asap, then hit A as fast as you can.
If a Sheik grabs at you when you run at them then dashdance in front of her and of course she'll whiff a grab. Dashdance is very good in general to just figure out what other people are doing, make them get nervous and keep pressure on them (just by running towards them), and lots of opponents will just be overwhelmed if your spacing is good. When they make a mistake (read: do anything) you can usually punish.
If you jump in and they shield, then try just jumping and not attacking. Every once in a while it's cool to see how effective NOTHING is. Vs opponents that shieldgrab a lot you can usually short hop in, fastfall behind them, and dash dance around their shield. Many people will roll away, spot dodge, or do something equally stupid considering you really never even planned on attacking. You can of course punish a predicted dodge/roll.
This is a big part of Cactuar's ridiculous mind****ing style. Stand near shielding opponents and wait for them to make a mistake. Options out of shield are limited, and people rarely choose good ones. He will typically dashdance away and grab if they aerial towards him OOS, hit them if they jump straight up or away from him, or grab if they dodge/roll.
Basically the moral of the story is:
-don't be predictable
-use your brain even if you don't want to
-wait for your opportunities
Just don't be the first to act and you'll be okay. And as always, more experience vs Sheik = you being better at the matchup. Try new things, try old things in unconventional ways, do stupid **** in friendlies, and work what you learn into your overall playstyle.