Sheik
Approach the sheik with patience. The sheik wants to grab you because hiss moves can be crouch canceled or easily out spaced. Crouch wave dashing in will get you to a safe space where needles aren't a threat and you can punish grounded needle charges. The Sheiks response to this is to full hop or short hop needle cancel or else they will start getting WOP'd. The mix ups here at this point vary. The sheik can empty hop grab, needle cancel into nair or needle cancel fair. Or they can just fair. The safer option for the Sheik, if you're playing your spacing game well, is for the sheik to throw needles, fast fall, and cover your landing from your fh aerial. I recommend stuffing them in the needle cancel animation or grabbing them out of aerial needles.
You can either shield the needles to attempt to shield grab the shiek (requires port priority), or read their jump and stuff it with a nair bair or fair (stuffing with nair can still lead to a counter attack from the sheik). You want them to throw these needles though and not needle cancel into an aerial.
Know when during the Sheiks jump that crouching is no longer an option and you need to shield. I recommend watching hbox vs shroomed. Figure out what makes them throw the needles and then out space and punish them. Rest their grabs and dash attacks.
Falco
I'm still researching this match up, but at our locals we have an up and coming puff challenging our third pr'd falco player who was an ex puff player. The puff will normally win the bo3, but the falcos adaption from losers will normally take it. This match up is an adaption in a nutshell. I can't give a complete and consolidated match up guide as I can for sheik since that is my practice partner, but I can illustrate stuff that does work.
Falco's dair will wreck jiggs in the air. They can also top platform camp very well. Staying in the falcos dj height range to catch their fast fall with an up air does pretty well. I've seen our local puff just spam up airs liberally. I've experimented with this too and the falcos will jump into this, they don't expect up air to out prioritize their moves. That's a free rest / fair combo to edge guard if they mess up the DI. Crouch the lasers and go for fade in / fade out nairs to catch their initial jumps.
Falco also has an aerial mix up game quite like Sheik. Falco has the ability to put a laser where an aerial will be and vice versa (Sheik can do this with needle cancel). PPMD does this pretty well and so does Mang0. Find out what makes them bair or nair instead of a laser, put your disjointed bair there, and hit them again. Crouch your landings and wave dash crouch approach. If you're in a situation where crouch wave dash under the lasers is being met with an fsmash or sh dair, dash back will be the laser so you can find a better spacing to approach (You might have to eat a laser or two, but the positioning is worth it). Rinse and repeat.
Edgeguarding a Falco is some what like Fox, except that if they have to Up-b they're done for. I would recommend covering stage and platforms and cover the ledge when you have a read on it. Tune into their habits.
I would like to edit this more once I play against more high level Falcos, but this is all I have no for the Match up.