I've cooked lots of farmed goose and duck over the years, and only a handful of wild birds, but in ovens not smokers.
To oven cook either, I put then on a cooling rack in a pan, so they don't stand in their own grease, (and there is going to be more grease than you can believe could possibly come out of that sized domestically reared bird).
Cooking them at 325 -350, prick them under the wings and over the breast area to allow any fat to run out. For wild birds, they don't have as heavy a fat layer, and I would think about either brining them or repeatedly basting them, covering them with bacon etc.
Cook them to temperature rather than time.
(((With farmed fowl cook them for 30 minutes, then start checking on them every 15 minutes, each time you check lift out the cooling rack or hold a towel tight to keep the bird in place, while you pour out and save the accumulated fat, keep checking them every 15 minutes, repeating the fat removal, when the bird has gone 15 minutes without producing more fat in the pan, your goose is cooked.)))
With wild birds cook for 30 minutes, then start checking every 15 minutes, each time you check lift out the cooling rack or hold a towel tight to keep the bird in place, while you pour out and save the accumulated fat, keep checking them every 15 minutes, repeating the fat removal, when the bird has gone 15 minutes without producing more fat in the pan, your goose is not yet cooked, (as a wild bird it had a lat less fat than a farmed bird), take the collected fat and baste the bird in it's own fat, then put it back for another 10 minutes, you may need to do these 10 minute bastes 2 or 3 times, check for internal temperature, I like to aim for 170 F, (final internal temperature), so you will want to take it off at 160 F +, and let it finish under a foil tent, so it will peak about 170 F ish!
Rest them 25 - 30 minutes, carve and serve.
If you are going to rotisserie them, keep a drip pan underneath and collect the fat, at 30, 45 & 60 minutes, at this point your wild birds may have run out of grease, begin basting and drop from 15 minute checks to 10 minute checks with additional basting.
