As was said, it's fine to feed dry.
I would keep a bottle of water in front of his stall so they can just sprinkle it over the feed when they give it, and would keep that bottle filler. Make it as convenient as possible for them
It is perfectly fine to feed it without wetting it. If it wasn't the bag would advise moistening it, which I am almost certain that it doesn't. Most people feed their TC without wetting it.
I honestly don't think that it's something you should bother the barn management about too much. It's important to really be careful about choosing your "battles" with barn management. You don't want to risk coming across as high maintenance and nitpicky. There's usually only a very limited number of extra "favors" that barn management are willing to do for you (unless you are prepared to pay more money for more services), so be really sure that this is so important to you that it overrides any other "favor" you might need from them in the future. Only ask them to change their routine for you if it is something especially important for your horse's health/wellbeing... and in this case I think that your horse will be fine with his feed being given to him dry.