What is a comfortable English translation of 姐夫 My soon-to-be sister-in-law is Chinese. My future wife is her older sister, so she doesn't feel comfortable calling me by my given name. In Chinese she would call be 姐夫, for which the nearest English translation seems to be "brother in law" or "husband of older sister", which is a bit of a mouthful to say the least. Even just "brother in law" is a bit much.

Is there are more appropriate term in English that I can suggest? I don't want her to feel uncomfortable.
The Chinese word 姐夫 is both a referent term and an address term. You can refer to someone as your 姐夫 (e.g. 我姐夫是中國人）as well as call him 姐夫 （e.g. 姐夫，你好嗎？）. 

The English equivalent "brother-in-law", however, is only a referent term. You can say "Peter is my brother-in-law" or "my brother-in-law is Chinese" etc., but I have never heard of anyone using "brother-in-law" as an address term (as in: How are you, Brother-in-law?) 

Here you are looking for an equivalent of 姐夫 as a direct address. I suppose the best way is for her to use whatever a normal English speaker would use to address his/her brother-in-law. In my understanding, this would be his given name or some kind of nick name that the brother-in-law would like to be called by. Addressing somebody as "Brother-in-law" would sound odd, IMO.