Definitely cross up whenever possible if you're going in on their shield. Most people will be able to shield grab you if you don't. Even better than attacking their shield though is to go for a neutral B. Command grabs are great, and if you space it well, it'll be difficult for them to ever punish you for it if they happen to dodge. If their shield is low, sometimes a d-tilt or d-smash will poke, but don't rely on those too much.
B-air works well to poke shields be nature of how wild its hitboxes are, and it helps if you cross up there too. Fair to single jab to rising nair works against a lot of people who are expecting double jab, but doesn't put you in a very good position (above them with your nair still out).
Overall, just try to be safe and unpredictable. That goes for a lot of Yoshi's neutral. And a lot of Smash's neutral, I guess.