I know you don't want to hear it, but the most effective tool in a Sheik ditto is the chaingrab. Second to that are tilts. It's pretty simple. However, after those is where people might disagree. I like to use lots of needles in that matchup...actually, I like to use lots of needles in every matchup, but back to the topic at hand. Bair is good in this matchup to keep the other Sheik at bay. Basically, whoever is better with Sheik will win.
Also, nobody is telling you to spam titls and grabs. If you go around the whole match trying to grab your opponent, they'll spot dodge and punish the lag (unless you JC, make sure to JC all your grabs). If you try to tilt the whole match, they'll just get behind you. You shouldn't be all elitist and say, "I'm too good for tilts and grabs, so I won't use one third of my character's attacks. They are cheap and beneath me." That makes you sound ********. No offense or anything, that's just how I see it. Tilts and grabs are a huge part of Sheik's game because (1) that's 1/3 of the available move slots and (2) they're awesome. If they're part of Sheik's game in her other matchups, you shouldn't neglect them in dittos.
Overall, my advice in this matchup would be basically the same as every other matchup: grab, tilt, and needle. Watch out for the opponents' grabs, be ready to spot dodge->dsmash/fair. Watch out for the opponents' tilts, be ready to shffl an aerial. Watch out for the opponents' needles, be ready to powershield/shield/jump/etc.
Edgeguarding is really important in this matchup too. Sheik has a ton of lag when she lands on the stage after an up-B. The best way to force her onto the stage is to edgehog. Then you can ledgehop->reverse fair or waveland->grab or whatever else you want to try.
Sorry for the semi-scatter brained post. I just typed as the thoughts were coming and didn't really plan out an organized post ahead of time. My bad. Oh yea, hope this helps by the way.