I think this MU has gotten significantly easier for us, though it's still not easy by any means.
The nerf to her needle range has been a pretty good change for us. She can't camp us as well, and leaf shield can now out range her. I'm not sure about item-thrown blades, but they impact needles anyway and would just get canceled by them. A shorthopped one might help if you have distance. I don't get the impression that Crash Bomb is useful in this case, but if you have the chance to land one on her, you may as well.
The fact that f-throw doesn't combo nearly as long as it used to is a huge benefit to us, as well as the fact that she no longer has her 50/50. According to ZeRo, her main kill options at this point are bouncing fish and upsmash, though we need to watch out for random Vanish mixups as well. This is great for us, as Mega Man's weight and fall speed typically made him incredibly easy for Sheik to combo into her previous kill setups. Now, although she can still rack damage on fairly well, she has to work more for kills...and since the Blue Bomber is pretty heavy, it means she has to work HARD for them and get more reads than before.
She's also 3 units lighter, which equates to us killing her significantly earlier (roughly 10%, I think?). Factor in the fact that her fair has a bit less range, and it's easier to space out with bair pressure, which has now become much more of a threat to Sheik since it's a great killing move.
Her downsmash was buffed to give it more knockback, but don't treat it any differently. It's still a highly punishable move and it's unlikely that Sheik users will employ it frequently, if at all (similar to our Flame Blast).
Also keep in mind that if a Sheik is pressuring your shield repeatedly with f-tilt, you can sneak an upper in. A lot of Sheik players don't expect this and think it's just free pressure, but that's not the case.
Keep tacking on damage whenever it's safe using blades, Leaf Shield (to also prevent being grabbed and locked into combos), and pellet mixups. Once Sheik is at 70%, she's at uptilt kill percent if Mega Man has zero rage. When you get grabs, pummel as much as you can before throwing to rack up damage. If you have distance, throw a leaf shield at her. Be mindful of bouncing fish, which almost every Sheik will go for at some point when you're coming back from off-stage. Mega Slide can also be good for getting her away from you if you can sneak it in between attacks.
Sheik will damage us a lot, but that gives us the rage we need to kill her earlier and safer. Just avoid getting killed as
Drarky
mentioned, get the damage in when you can, and we can definitely make this matchup work more consistently. She can still gimp well, so play it safe. I wouldn't even go off-stage against her unless it was to drop a blade or something. It's likely better to throw LS on and try to get some damage as she goes for the ledge.