I think the real issue is not with the SIL, but rather with the wife. It sounds like the wife wants to do the gift, but because the cost is too much, she is trying to use the loan to avoid the focus on the high priced gift.
You think $200 is too much for a gift, your wife disagrees. Only you and your wife can settle this part. We here at MMM can only say what we would do, but your situation is unique to you. If you settle this matter first, the loan becomes simpler to consider. My in-laws have done so much for us I would not think twice about spending that on a useful gift for them. Like you I also frown on gifts just for gifts sake, so we all agreed to stop exchanging gifts between the siblings about 5 years ago, and that has worked well.
Here is how I look at the loan part: If you loan a friend $50 and you never see the $50 or the friend, you got a GREAT DEAL, saving possibly thousands on a friend that turned out to be not so great of friend to begin with.
This happened to me 2 times in my life, once for $50 and once for $20. Never heard from the $20 again, but the $50 called me years later asking for a job from my father. I said sure, I would recommend him right after he gave me the $50 back. THEN I never heard from him again.
I know it is different with family, but at some point after non-repayment you could still chime in and say something like "we know you do not have the money, so we consider that a gift to you, and NEVER ask for money again".