The only problem you'll have is that he will get all the rich food that the does will need, and he'll take up the space/resources of a productive animal in the herd. If you want a tame animal, does can be very tame. Most of my dairy goats won't leave me alone if I'm in the pasture.
Are your does a dairy breed? I would breed your does to a dairy buck. Pull the daughters and raise them on the bottle a few days after they're born. If you take them at 3-4 days of age, you can go right to a 3x per day feeding schedule and don't have to worry about colostrum etc. The kids transition to the bottle just fine at that age. Then, you can either sell their dams or keep them - you'll have tame goats to raise for milk/pets. You could still breed the untame does and continue to take daughters and let them dam raise the boys for meat, or you could just breed them meat to make them almost totally hands-off. The bottle babies will not leave you alone, so tameness will not be an issue.

It doesn't have to be super time consuming, and the schedule for bottle feeding can be quite flexible.
If you want to try to break the wild goats to the milkstand, start getting your does used to a grain ration on the stand NOW. Doesn't have to be a large amount. If you're thinking of breeding, now would be a good time to start as a 'flushing'. Do not wait until they freshen and expect them to take right to it! Even my bottle babies I start putting in the milkstand a month pre-kidding and start massaging their udder/pretending to milk. Using this method, all FF'ers I've broken have transitioned seamlessly to the milkstand procedure after kidding.
Personally, after you get some replacement daughters, I'd breed their dams so that they're bred for meat, so that they and their kids can keep being wild. I handle my wild boer does just a few times per year- trim hooves 4+ times per year, and copper bolus/BoSe pre breeding and pre-kidding. I observe all kiddings and make sure no issues arise. Help them dry kids if born in the cold - otherwise, they're hands off and that's fine for me. I don't need to pet all my goats - I don't have that many hands.

If they have boys, leave them on (or breed to boer and leave all kids on). If they have dairy daughters, keep pulling and raising on the bottle.
I don't like dam raised kids for the milkstand, either. I bottle raise all dairy kids. It means I can get rid of the wethers cheaply and fast, and the does are sold friendly on the bottle and the ones I keep are super friendly.
Wethers have no odor. The only time I saw a wether that peed on himself and stank was a monorchid who still had a teste in his body cavity. He had to have surgery to get the 2nd teste. He probably wasn't very fertile, but the testosterone production was still higher. This is NOT common though.
As for not keeping a buck - I find it's an extreme headache not to, unless you know of someone very close by. And are really good at spotting heats and know when to take the does to the buck (harder when the does don't have a buck to holler at/flirt with). I suppose you could also lease a buck for a month, but that has it's only list of difficulties. If managed properly, they're more a convenience than an inconvenience. They don't have to be your friend. I don't hang out with my bucks that often. Pen them with a wether-buddy far from the house.