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One thing you can do to help out is by expanding the edges of the textures. For example, we had a similar problem with our RenderCrate fern assets, and so expanding the colour of the texture outside of the border helped hide any of the black background 😀
Personally, I'd say to get the cleanest render, painting it manually with skin/lip/hair materials would be best! That way there won't be any pre-baked lighting issues 😀