Tux rental companies with locations in the US and in Peru?
Not going to happen. Taking the measurements is a reasonable plan because the local tux place will likely have adjustable pants, and similar coat sizes in the same style and color as you are wearing. Even if a tux chain had an office in Peru, there still would be no guarantee his tux would match.
Have him go to a tux shop, get measured and TRY ON a tux. Then send the results to your local tux shop. The pants have adjustable waists and can be hemmed in about 30 minutes. The jacket is the tough part. And don't pick anything unusual. Just get a black tux because they'll have the most of those in stock.