Can you use a putter in place of the pin to show the hole location for your playing partner?
You sure can! But you must treat the putter (or whatever else you have to mark the hole) in exactly the same way as you would the pin, according to Rule 17 which begins:
17-1. Flagstick Attended, Removed or Held Up
Before making a stroke from anywhere on the course, the player may have the flagstick attended, removed or held up to indicate the position of the hole.
If the flagstick is not attended, removed or held up before the player makes a stroke, it must not be attended, removed or held up during the stroke or while the player’s ball is in motion if doing so might influence the movement of the ball.
There’s more details concerning the pin or flagstick. Head on over the the Royal and Ancient website for all the rules.