According to this, the run completes 86/96 exits. It's "no powerups", which includes no Yoshi and no switch palaces either.
For the curious, the 10 exits that aren't made in this run:
The 4 Switch Palaces, which are completable as Small Mario, but are counted as "Powerups" and so are skipped
The secret exit to the first Ghost House (requires flying with the cape), which leads to a bonus level
The secret exit to Cheese Bridge Area (requires either the cape or Yoshi to go underneath the main exit), which leads to Soda Lake
The exit to Soda Lake, which you can't get to because of the previous item
Both exits from Star World 1 (filled entirely with blocks you have to break by spin-jumping on them). A Mushroom is provided at the start.
The secret exit to Valley of Bowser 4 (requires using Yoshi to collect an item through an unbreakable wall with his tongue), which leads to one of the entrances to the Star Road bonus levels
Notably, none of these are on the "main path" through the game; almost all of them lead to "bonus" content of one form or another.