There's nothing that's gonna replace Warhorn specifically. But you do have access to Colossus on Necro, which isn't bad at all. Depending on what content you wanna end up doing you may need to get Warhorn in the end(try claiming AP daily login bonuses on this character also; it's not fast but it's free AP). But if no one is requiring it of you, or you're pugging, you're certainly free to use Colossus. Just make sure to time it right, as you're definitely using it more for the debuff than the damage itself (IDK how good the colossus damage is on necrotank honestly).
There's also resto-staff ult, but that's only an option in 4man content and my gut says Colossus would end up more efficient. May depend on the group tho.
Alliance Point Reward Tiers
First Place - 12000+ AP + an extra champion reward through mail.
Second Place - 10000+ AP
Third Place - 7250+ AP
so like 4 Battlegrounds coming in last place will earn you warhorn. They only last 15 minutes at top. 1 hour total not counting waiting for a match. Easy to obtain it.
just repair walls in Cyro, it will take (with some luck) 10-15 minutes to safety get War horn. No encounters with hostile players.
However, you totaly don't need that skill if you aim for PUG dungeons any diffuculty. War horn is super meh for such content. Use self survive ultimates instead. The best tank is one who can stay alive no matter what. I use Temp Guard (front) and Magma shell (back) on my DK tank. I don't need a healer, i can take ton of damage while ressurection other players.
Oh, and since you are Necro tank, that Necro ressurect ulti is 100 times better than War horn )
For dungeons, again.
Use Colossus on one bar and the 3 person rez on the other bar. I've run in groups where both of these are asked for as a tank. However you are gimping the group if you don't have Warhorn on at least one bar because that is a necessary group buff for some of the harder content.