CASE refinish, YES OR NO?

[NIHO]

My 116710 is 12.5 years old. It underwent 1 RSC service with polish 5.5 years ago and was disappointed that the sharp edges were a bit rounded. Now I have a choice of doing a case refinish at a very reputable independent refinisher. My problem is that the watch is very well worn (and also I brushed the bracelet). Will the watch look weird if it has a beat up bezel and bracelet (which I like the patina look) and then a new looking case (albeit with better lines). Here are some pics...so yes or no? The watch runs at +1.3s/day so no reason for movement service.