lol
Anybody can do that. Probably better than Yoshi even, because he can't attack very well out of Shield. Attacking out of dodge is a different story, however, everybody else can do that too. XD
I would only dash-in-shield with Yoshi after a successful d-tilt against an opponent in 40-ish %. Otherwise, your best bet out of dash is:
1. Dragonic Reverse Landing + (d-tilt / AA / Dsmash / f-tilt)
2. Turn around -> SH Bair + good air control vs. Shielders
3. Dodge -> something fast
4. Dodge Roll -> something fast
5. Jump behind them with any aerial, preferably Bair or Dair
6. Air Dodge behind them -> something fast
7. Jump -> Egg Lay (good against people who just Shield all your Aerials)
8. Sweet-spotted SH Nair (basically, sliding you thumb from Y to A with your Control Stick in neutral) + good air control to avoid Shield Grabs, if needed
9. Hyphen Smash at high %'s
10. Yoshi Bomb at high %'s
These are the best options you have, IMO, to approach with Yoshi, from best to worst. Somethings will work better on different characters, and sometimes NOT approaching is a better option against certain characters. And this is when the opponent is NOT knocked-down. You can do much more rewarding stuff in such a situation. Like, I don't know, run past them and pivot-grab into CG? lulz
Finally, as always, don't be predictable.