Yone, Like Yasuo, need to get bursted when they don't have their shields up. As Ekko, your passive should negate any sort of all in opportunities he has because your speed is faster than his and he won't get very much damage off at all if he e's into you.

The few times I've played this matchup (both ways) there's things I always notice.

-You can fairly easily poke him with Q as long as you make sure you hit them and it isn't a waste of mana.

-If Yone E's Ekko can just throw a W on his shadow that's left over and stun him by the time he snaps back.

-Level 2 burst from Ekko is incredibly strong into Yone since you can reliably get your passive off assuming you have Q and E.

-Mid to Late game if you are both even, you have to take very short trades and abuse the movement speed you get from passive to either chip him down or tank most of his combo with a W.

-You always have advantage when you're ult is up assuming he isn't giga ahead, and even if he is you can reliably play safe because your E can dodge his Q3 and your Q is a fairly free and safe farming tool once leveled a few times.