I don't think the sinew would harm the hickory, but hickory is already sensitive to humidity, add sinew to that mix, and it could change draw weight considerably based on humidity levels. For a hunting bow out of hickory, I would do it without sinew (unless it is a really short bow with static tips, then I am all in on sinew).
You should be able to make a good weight/performance bow from just the hickory. It is a strong wood...
Silk backing can look really good, and will offer protection, so +2 on that.