Teaching him will also be a learning experience for you, my husband is half Vietnamese and Laos and I am Mexican our son is mixed with all that so as he grows well teach him all 3, my husband was mostly brought up Lao in the aspect of going to the temple here and there but aside from that he is very vanilla to it as well. I see it as a learning experience to not only show and embrace the roots that my son has but also know for our own understandings. Yes we won’t practice the ways intended but him being aware is always good. And that’s with any culture my best friend who I’ve known for years is Korean and she helps me teach my son Korean and I get to learn to. Regardless of it coming naturally or not just do what you feel comfortable.
I think it is very important to expose atleast the basics maybe through books or music or shows when at appropriate age because that helps with a sense of identity in the long run. Last thing you want is your kid growing up to be just another teenager struggling to find/understand themselves and their identity and then blaming you for it. Maybe it could be something you guys explore together to bring you guys closer and to show that you are considering their future and journey to adulthood.
I don't have quite the same problem as I was born in the UK raised by Chinese parents. But I wanted to teach my daughter the language which at best have very broken vocabulary. I was planning to learn with her some mandarin and brush up on Cantonese. I don't think theres anything wrong with learning at the same time. I think it'll help any identity problems in future and be a bonding experience :)
I plan on teaching my kids about their cultures white, black and Mexican but by any means they do not have to embrace all of them if they don't want and if they aren't Interested in it I'm not gonna waste time teaching them something they ain't paying attention to, but they will naturally learn about each just from exposure so its not really a big thing.