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.
In English, respect can be shown by calling someone by their title, followed by last name. So, if you were named Smith, she could call you Mr. Smith, or Dr. Smith, or Professor Smith, etc.
I would also explain to her that your community's tradition is to address all brothers-in-laws by their first name and that you and your family will be honored if one day she feels comfortable to do it.
If you go over just calling name. Simply "Brother-in-law".
Now you know the limits of English.
If you're marrying her older sister, you're not her older sister's brother-in-law. Little Sister is calling you "Sister's Husband".
My cousins in Asia address me as 姐姐，and for fun, they'd call my husband "Jeff". They speak Mandarin for the most part. When interacting with us, they definitely use 姐夫。I believe when not interacting with us, they refer to him by his name, which makes sense to me. My younger siblings and cousins in Canada have no problem addressing my husband by his first name. However, when they do greet me in Cantonese/Mandarin, I've noticed they will also greet my husband as 姐夫。 I don't believe there's a straight answer. Whatever makes you, your future wife, and your future sister-in-law most comfortable, will be the best solution for you guys.
In US, I would suggest you call your “姐夫” directly by name. In China, that may sound disrespectful when age difference is too big.
