If you don't mind some suggestions:

Been playing Snake Pass and it's a good example.
I think Captain Toad: Treasure Tracker also counts.
DK: King of Swing doesn't have a jump button but holding L and R and releasing does a jump attack.

Also doesn't Pitfall! have a jump button? Is this in reference to a specific version?

@DeltaWDunn great suggestions, thanks! I don't know why I thought that about Pitfall; I just remembered the vines swinging back and forth, but you're totally right.

Raven's Hike (which only uses a grappling hook to move around) should fit the bill here.

getting over it with bennett foddy?

Bomberman 64, Sexy Hiking (like Getting Over It).

@Drax @Gliscor @Lot0 all added; thanks!

the last tinker says "It's Mimimi's take on all-time classics like "Jack and Daxter" or "Banjo-Kazooie", while breaking the mold by not having a jump button."