Have you tried a straw cup?
I was going to suggest this too.
I bought a few different straw cups and tbh in the end settled with just a bottle and those long bendy disposable straws because straws are so hard to clean and I always worried about milk residue in them...but I'm going off topic...DS refused to have his morning milk moved to a sippy cup but was happy with a straw and will take a full amount. He has a milk with dinner/supper in a sippy and only takes 1 or 2 oz.
We had no issue swapping to cows milk at all. I just gave it to him just under the 12 months guidance because there was none of our formula left in any shop in town! he didn't bat an eye. I think all LOs are different and some don't like the change over and some don't mind.
Hope it goes smoothly for you.