Yep it’s a reasonable approach, though it all depends on how you want the movement to work. Triggers are good if you want the ladder climbing automatically activated whenever the character gets to one end of it. If the player should activate climbing directly, you can do a test for proximity/direction of the ladder.
For the movement, in your PhysCustomClimb you can process the player’s input and apply movement to the character along the ladder’s direction vector as appropriate.