The power of a Neder is only to Assur you from Hana’a if you are Oiver on the T’nay. So, just don’t bring your Korban when you are not allowed to, and then Yir’eh Ad Sheyisto’av.
If you made a Shevua that you’ll be mock-Makriv it then Ein Shvua Chal Ashvua.
I just don’t understand how you get spiritual inspriration from being Mekayem your Nedarim and Shvuoas. After all, Tov Asher Lo Tidor. But if a Goy does it, he can bring a real Korban.
My only Shaala is if a Goy being Makriv a Korban in Chutz La’aretz for the Kappara of a Yid, does it help? What if it is a Mum that is Kosher for them and not for us? What if it is a bird other than Tor or Bnei Yona?