Maybe have a new faction that's somewhat similar to the Knights of the Nine (KotN) would be more welcoming to Skyrim. I don't want to see the KotN specifically brought to Skyrim because Umaril is supposedly defeated and gone for good, so if the KotN are brought to Skyrim, what purpose would they serve? Aiding the Dovahkiin?
The reasons can be heard in some of their post quest banter:
1) Starting a crusade. Liches, Vampires, and other forms of evil are enough incentive
2) Finding relics of sacred power
- The Boots of the Apostle belonged to Tiber Septim, who ascended to Talos/Ysmir
- The Lord's Mail is an artifact created by Kynareth
- Stendarr's Hammer
- Even the Chrysamere, while not proven to be a holy relic, is implied to be one
If any of these relics were in Skyrim, you can bet the Knights would go for it