Couldn't you just do this with a regular for loop and a few datatypes/functions? (This pseudocode is an Elm/Haskell/Rust/TypeScript-inspired abomination, but pretty portable to any language...)
type Node = { value: Any, left: Node, right: Node }
type Direction = Left | Right
type TreePosition = { root: Node, currentNode: Node = root, position: Direction[] = [] }
# Implementation left as an exercise but should be obvious and run in O(1), I believe. Returns Nothing when we're out of nodes.
function nextPosition(position: TreePosition): Option<TreePosition>
# The tree you want to iterate through
const myTree: Node = ...
# The loop
for(let position: TreePosition? = TreePosition(root: myTree); position != Nothing; position = nextPosition(position) {
node = position!.currentNode
# Your loop code
}